RARE EARTH DOPED CRYSTALS FOR CLASSICAL AND QUANTUM INFORMATION by Philip Joseph “Tino” Woodburn A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Material Science MONTANA STATE UNIVERSITY Bozeman, Montana June 2021 ©COPYRIGHT by Philip Joseph “Tino” Woodburn 2021 All Rights Reserved ii TABLE OF CONTENTS 1. INTRODUCTION TO RARE EARTH IONS .............................................................................1 Background of Rare Earth Ions in Solid State Materials Fabrication and Characterization ....................................................................................................................1 The 4f Electrons of Rare Earth Ions ....................................................................................1 Resonant Linewidths of REI in Crystals ..............................................................................5 Outline of Dissertation .................................................................................................................6 2. RARE EARTH ION DOPED MATERIAL PROPERTIES ........................................................9 Survey of Materials Studied.........................................................................................................9 Rare Earth Doped Single Crystals .............................................................................................10 Er3+:Y2SiO5 ........................................................................................................................10 Tm3+:Y3Ga5O12 ..................................................................................................................12 Yb3+:YVO4 .........................................................................................................................12 Er3+:Y3Al5O12 .....................................................................................................................16 Rare Earth Doped Powders ........................................................................................................17 Tm3+:Y3Al5O12 ...................................................................................................................18 Tb3+:Y3Al5O12 ....................................................................................................................20 Er3+:LiNbO3 .......................................................................................................................21 Synthesis of Rare Earth Doped Crystals ....................................................................................22 Single Crystal Fabrication..........................................................................................................23 Czochralski Method ...................................................................................................................24 Parameters of CZ Growth Technique ................................................................................24 Powder Synthesis of REI Doped Materials ...............................................................................25 Pechini/SolGel Chemical Synthesis of Powders................................................................25 Co-Precipitation .................................................................................................................25 Mechanical Processing of Single Crystal to Powder .........................................................26 Powders Post Processing....................................................................................................26 Summary of REI Doped Material Properties .............................................................................27 3. CHARACTERIZATION METHODS AND EQUIPMENT .....................................................28 Overview of Characterization ....................................................................................................28 Optical Spectroscopy Equipment ...............................................................................................29 Optical Components...........................................................................................................29 Cryostats ............................................................................................................................31 Materials Characterization of Resonant Frequencies through Optical Spectroscopy .................................................................................................................32 Absorption and Fluorescence .............................................................................................33 Spectral Hole Burning........................................................................................................36 iii TABLE OF CONTENTS CONTINUED Photon Echoes ....................................................................................................................37 Electron Spin Coherence....................................................................................................39 Powder Characterization Techniques ........................................................................................38 XRD ...................................................................................................................................38 Scanning Electron Microscope ..........................................................................................39 Single Crystal Orientation..........................................................................................................40 Birefringence......................................................................................................................40 Laue x-ray ..........................................................................................................................41 Acid Etching ......................................................................................................................42 Chemical Composition.......................................................................................................43 Summary ....................................................................................................................................46 REFERENCES CITED ..................................................................................................................47 4. USING BIREFRINGENCE TO ORIENT CRYSTALS FOR CLASSICAL AND QUANTUM INFORMATION APPLICATIONS ..........................................................50 Contribution of Authors and Co-Authors ..................................................................................50 Manuscript Information .............................................................................................................51 Abstract ......................................................................................................................................52 Introduction ................................................................................................................................52 YSO’s Dielectric and Crystal Axes ...........................................................................................53 Location and Identification of the Extinction Axes ...........................................................54 Direction of the b-axis .......................................................................................................56 Using a Conoscope to Locate and Identify the Axes .........................................................57 Biaxial Crystals: Monoclinic, Triclinic, and Orthorhombic Systems ........................................58 Uniaxial Crystals: Tetragonal, Trigonal, and Hexagonal Systems ............................................59 Isotropic Crystals: Cubic Systems .............................................................................................60 Conclusion .................................................................................................................................61 REFERENCES CITED ..................................................................................................................57 5. ELECTRON SPIN COHERENCE IN OPTICALLY EXCITED STATES OF RARE-EARTH IONS FOR MICROWAVE TO OPTICAL QUANTUM TRANSDUCERS .................................................................................................62 Contribution of Authors and Co-Authors ..................................................................................63 Manuscript Information .............................................................................................................64 Abstract ......................................................................................................................................65 Introduction ................................................................................................................................65 Coherent Raman Heterodyne Scattering ....................................................................................67 Excited State Spin Echoes .................................................................................................67 Exited State Scheme for Optical to Microwave Transduction...................................................68 Conclusions ................................................................................................................................69 iv TABLE OF CONTENTS CONTINUED Acknowledgments and Funding ................................................................................................69 References Cited ........................................................................................................................69 SUPPLEMENTARY MATERIAL ................................................................................................71 Experimental Methods ...............................................................................................................72 Optically Pumped Excited State Population ..............................................................................74 Spin Echo Decay Modeling .......................................................................................................75 Estimation of Relaxation and Decoherence Rates .....................................................................76 Excited-State Spin Lifetimes vs Temperature ...........................................................................79 Instantaneous Spectral Diffusion ...............................................................................................80 Low Temperature Modeling ......................................................................................................80 References Cited ........................................................................................................................81 6. MEASUREMENT OF THE THULIUM ION SPIN HAMILTONIAN WITHIN A YTTRIUM GALLIUM GARNET HOST CRYSTAL ...........................................81 Contribution of Authors and Co-Authors ..................................................................................81 Manuscript Information Page ....................................................................................................82 Abstract ......................................................................................................................................84 Introduction ................................................................................................................................84 Spin Hamiltonian for the Enhanced Zeeman and Quadratic Zeeman Effects ...........................85 Crystal Symmetry and Site Selection ........................................................................................85 Experimental Setup ....................................................................................................................86 Spectral Hole Burning Description and Results ........................................................................87 ODNMR Measurement and Results ..........................................................................................88 Verification of Results ...............................................................................................................89 Linear Zeeman Shift ..........................................................................................................89 Quadratic Zeeman Shit ......................................................................................................90 Optical Clock Transitions and Special Directions .....................................................................90 Conclusion .................................................................................................................................91 Acknowledgments......................................................................................................................92 REFERENCES ..............................................................................................................................92 SUPPLEMENTARY MATERIAL ................................................................................................94 Fitting Details.............................................................................................................................94 Secondary Fit of the SHB Difference Tensor ............................................................................95 Secondary Fit of the ODNMR Directional Tensor ....................................................................95 Minimize the Spin-Inhomogeneous Broadening .......................................................................96 Branching Ratio Simulations and Directions .............................................................................97 References ..................................................................................................................................97 v TABLE OF CONTENTS CONTINUED 7. CHARACTERIZATION OF 171Yb3+:YVO4 FOR PHOTONIC QUANTUM TECHNOLOGIES .............................................................................................101 Contribution of Authors and Co-Authors ................................................................................101 Manuscript Information Page ..................................................................................................103 Abstract ....................................................................................................................................104 Introduction ..............................................................................................................................104 Background ..............................................................................................................................105 Material Properties ...........................................................................................................105 Spin Hamiltonian .............................................................................................................106 Experimental Methods .............................................................................................................106 Optical and Spin Properties of 171Yb:YVO4 ............................................................................107 Optical-Absorption Spectroscopy ....................................................................................107 Optical Transition Strengths ............................................................................................108 Excited-State Lifetimes ....................................................................................................108 Optical Coherence Measurements ...................................................................................108 Nuclear Spin Measurements ............................................................................................109 All-Optical Spin Coherence Measurements.....................................................................110 Summary and Conclusions ......................................................................................................111 Acknowledgments....................................................................................................................111 References Cited ......................................................................................................................112 8. OPTICAL SPECTROSCOPY AND DECOHERENCE STUDIES OF ERBIUM DOPED Y3Al5O12 AT 1.5 MICRONS .............................................................114 Contribution of Authors and Co-Authors ................................................................................114 Manuscript Information ...........................................................................................................116 Abstract ....................................................................................................................................117 Introduction ..............................................................................................................................117 Crystal Field Level Structure of 4I 4 13/2 and I15/2 .......................................................................118 Excited-State Lifetimes ............................................................................................................118 Inhomogeneous Broadening of the 4I13/2 and 4I15/2 (Y1) Transition .........................................119 Thermal Broadening and Frequency Shift ...............................................................................120 Linear and Quadratic Zeeman Effect .......................................................................................120 Optical Coherence Lifetime Measurements .............................................................................124 Spectral Diffusion at Long Timescales ....................................................................................127 Conclusion ...............................................................................................................................127 Acknowledgments....................................................................................................................128 References ................................................................................................................................128 vi TABLE OF CONTENTS CONTINUED 9. EFFECTS OF FABRICATION METHODS ON SPIN RELAXATION AND CRYSTALLITE QUALITY IN Tm-DOPED Y3Al5O12 POWDERS STUDIED USING SPECTRAL HOLE BURNING ................................................................130 Contribution of Authors and Co-Authors ................................................................................130 Manuscript Information ...........................................................................................................132 Abstract ....................................................................................................................................133 Introduction ..............................................................................................................................133 Experiment ...............................................................................................................................134 Tm:YAG ..........................................................................................................................134 Spectral Hole Burning......................................................................................................134 Bulk Single Crystal Reference .........................................................................................134 Results ......................................................................................................................................135 Crushing and Ball Milling ...............................................................................................136 Effects of Annealing ........................................................................................................136 Comparison of High- and Low-Energy Ball-Milling Methods .......................................137 Direct Chemical Synthesis ...............................................................................................138 Discussion of Different Characteristics Methods ....................................................................139 Conclusions and Outlook .........................................................................................................139 Acknowledgements ..................................................................................................................139 Disclosure Statements ..............................................................................................................139 Funding ....................................................................................................................................139 References Cited ......................................................................................................................140 10. EFFECTS OF MECHANICAL PROCESSING AND ANNEALING ON OPTICAL COHERENCE PROPERTIES OF Er3+:LiNbO3 POWDERS .......................141 Contribution of Authors and Co-Authors ................................................................................141 Manuscript Information ...........................................................................................................143 Introduction ..............................................................................................................................144 Sample Preparation ..................................................................................................................145 Optical Coherence Lifetime .....................................................................................................147 Two Pulse Photon Echoes ................................................................................................148 Echo decays in powders of randomly orientated crystallites ...............................149 Magnetic field dependence of coherence lifetimes ..............................................149 Spectral Hole Burning......................................................................................................150 Free Induction Decay and Spectral Diffusion ..................................................................151 Conclusion ...............................................................................................................................152 Acknowledgements ..................................................................................................................153 REFERENCES CITED ................................................................................................................154 vii TABLE OF CONTENTS CONTINUED 11. MODIFICATION OF RELAXATION DYNAMICS IN Tb3+:Y3Al5O12 NANOPOWDERS ........................................................................................155 Contribution of Authors and Co-Authors ................................................................................155 Manuscript Information Page ..................................................................................................157 Abstract ....................................................................................................................................158 Introduction ..............................................................................................................................158 Experimental Details ................................................................................................................159 Time Resolved Fluorescence Measurements ...........................................................................141 Measurements of Temperature-Dependent Population Re-Distribution .................................162 Conclusions ..............................................................................................................................163 Acknowledgements ..................................................................................................................163 Appendix A: Powder Characterization ....................................................................................164 Appendix B: Spectroscopic Investigations of Powder Quality................................................164 Appendix C: Local Temperature Measurements .....................................................................164 References Cited ......................................................................................................................165 12. SOLID-STATE LASER COOLING OF OPTICALLY LEVITATED PARTICLES ..........................................................................................................................167 Contribution of Authors and Co-Authors ................................................................................167 Manuscript Information Page ..................................................................................................168 Abstract ....................................................................................................................................169 Introduction ..............................................................................................................................169 Radiation Forces ......................................................................................................................169 Radiometric Forces and Importance of Cooling ..............................................................171 Material Science & Cooling Demos ........................................................................................172 Bulk Cooling Theory .......................................................................................................172 Bulk Cooling Demonstration of Yb:YAG .......................................................................172 Fabrication of Doped Particles.........................................................................................173 Thermometry Demonstration ...........................................................................................174 Optical Trapping Experimental Setup .....................................................................................174 Launching Microspheres ..................................................................................................174 Horizontal Dual-Beam Optical Trap ................................................................................175 Conclusions/Future Work ............................................................................................................176 Acknowledgements ......................................................................................................................176 References ....................................................................................................................................176 13. Summary ................................................................................................................................177 REFERENCES CITED ................................................................................................................179 viii LIST OF TABLES Table Page 3.1. Full Impurity scan of Tm:YGG crystals using LA-ICP-MS using the Teledyne Photon Machines Iridia system. .............................................................................................48 6.1. Spin Hamiltonian values. The gj values are calculated using the general formalism described in [14]. The AJ values are from [7] and can be recalculated from [14] as they depend only on the expectation value for electron radius for this Tm transition. gx;y;z values for the excited and ground states are measured in this work. Together with the listed constants they allow calculating all ΛJ,α; values using Eqn.5. .......................91 6.2. Optical clock transitions with angular coordinates of ~B given relative to the (<100>,<010>,<001>) crystalline axes. These positive and negative projections are based on the unit cell directions for the 6 sites for the Tm:YGG. ..........................................94 6.3. Defined directions in the crystal. These directions were normalized to compute all projections of the magnetic fields. The positive and negative axes are assumed by convention to keep the site z directions pointing into the unit cell. .......................................96 7.1. Absorption properties of the 171Yb3+:YVO4 transitions as labeled in Fig. 7.2, including the transition polarization [161], integrated absorption coefficient, oscillator strength, and radiative decay rate at zero magnetic field. ....................................108 8.1. Crystal field levels of the ground 4I (Z ) and excited state 415/2 i I13/2(Yj) multiplets in 0.1 % Er3+:YAG (in cm-1), including previously reported values from Refs. The last column shows our measurements of the relative strength of the transitions, with the branching ratio (i.e. the relative intensity I/Itot) for the 4I13/2(Y1)) 4 → I15/2(Zi) fluorescence and the peak absorption coefficient in cm-1 for the 4I 4 15/2(Z1) → I13/2 (Yj) absorption transitions............................................................................................................119 8.2. Linear and quadratic Zeeman coefficients determined from Fig.8.7 for each pair of transitions (positive and negative number) for B||X. From the linear part we calculated an averaged Δg that can be equal either to gg + ge or |gg - ge|for respectively the cross and spin-preserving transitions. We attributed gg values to each pair of transitions and deduced the ge values for the excited state doublets. See main text for more details. ....................................................................................................123 8.3. Parameters for transition 1 (see Fig. 8.7), extracted from the fits to the two pulse photon echo experiments of Fig. 12. ....................................................................................126 8.4. Spectral diffusion parameters extracted from the fits to the three pulse echo data for transition 2 shown in Figure 8.7. ..........................................................................................127 9.1. Hole widths (Γ) (bold font indicated visible side holes), and lifetimes (Ta) of all measured materials at 1.6 K and B = 1 T. ...........................................................................135 10.1. Powders characterized in the manuscript and their fabrication methods. ..........................146 ix LIST OF TABLES CONTINUED Table Page 10.2. Parameters from fitting the experimental data shown in Fig. 4 by Eq. (4). For all samples, the value of Γ max was fixed to 1MHz and the parameter Γ0 was constrained to be larger or equal than minimum bulk value (Γ0 = 3 kHz at 6 T), which lead to Γ0 = 3 kHz . ..............................................................................................................................149 10.3. Maximum effective absorption coefficient αeff extracted from SHB measurements, as well as effective linewidths Γeff extracted from SHB (after Tw=25 µs), 2PE (heterodyne measurement for samples #3 to #6) and FID (after a T=5 μs) measurements at T=1.6 K and B= 2 T for different samples. When a double exponential decay was observed, as described in the main text, both decay values are listed. For the bulk crystal, the magnetic field and light polarization were parallel to the c-axis (B∥E∥c). ...............................................................................................................150 x LIST OF FIGURES Figure Page 1.1. Illustration of the perturbations affecting the energy levels of 4fN configurations in lanthanide ions. .........................................................................................................................2 1.2. Dieke Diagram showing energy levels of the trivalent rare earth ions erbium, thulium and ytterbium. The red arrows signal the transitions in use in this thesis. The diagram is scaled in wavenumbers and wavelength along with the visible spectrum being marked in color. ...................................................................................4 3.1. Image of a Coherent 699 Dye ring laser being pumped with a 532 nm laser. ........................30 3.2. Five different cryostats used in this work. Top Left: Montana Instrument’s C2 closed cycle Gifford-McMahon system. Top Center: Oxford SpectrumMag helium bath cryostat. Top Right: PhotonSpot’s helium sorption fridge. Bottom: Cryomech’s closed cycle pulse tube in the silver cylinder and Roger Macfarlane aligning a beam through an Oxford Optistat. ....................................................................................................34 3.3. Absorption spectra of the 3H4 levels of 3%Tm:YGG. ............................................................37 3.4. Block diagram of two pulse photon echo experiment where the area of the echo is measured as a function of the t12 pulse delay. As the pulse delay is increased the area of the echo is measured. .........................................................................................................38 3.5. Two Pulse Photon Echo decays of four different Tm:YGG growths all taken in an Oxford liquid helium bath cryostat at 1.2K. ...........................................................................39 3.6. XRD spectra of Tm:YAG powder taken in ICAL. The red lines are positions of prominent peak of a YAG reference material. .......................................................................41 3.7. Electron microscopy images of Tm:YAG powders. Left: Images showing a larger field of view of the powders, the inset showing a typical amount of material produced from a single production run. Center: A closer view of the well-defined dodecahedral YAG crystal powders. Right: powders partially melted after being heat treated in metal-halide flux. ....................................................................................................42 3.8. Birefringence photographs of LiNbO3. Left: Looking along the optical axis, the c- axis of LiNbO3. Right: Looking along a vertical extinction axis, the optical axis can be seen in the top of the image, showing how a crystal that is not cut along the optical axis looks between crossed polarizers. .......................................................................43 3.9. The backscatter reflection points of YSO observed with Laue X-rays. Left: The image is overlaid with the simulated points using Orient Express software to determine the orientation of the crystal. Right: The backscatter photo showing the orientation of the crystal axes with respect to the reciprocal lattice points and the dielectric axes. ........................................................................................................................44 xi LIST OF FIGURES CONTINUED Figure Page 3.10. Microscope image of etched surface of a {110} plane perpendicular to the <211> axis of a Tm:YGG sample. The etch was done with phosphoric acid for 1 hour at 200 C. .....................................................................................................................................45 3.11. Concentration of impurities in three different Tm:YGG crystal growths using the Iridia Teledyne Photon Machines Laser Ablation Inductively Coupled Plasma Mass Spectroscopy...........................................................................................................................47 4.1. The optical plane and axes of YSO, showing a positive biaxial crystal with a 2V angle of ~40 degrees. ..............................................................................................................54 4.2. The crystal axes (solid colored lines), and the dielectric axes (black lines, horizontal and vertical) overlaid with the Laue x-ray points of YSO. The reciprocal lattice vectors (dotted colored lines) observed using Laue x-rays reflection photographs show D1 is about 23 degrees from the crystallographic a-axis, and D2 is about 11 degrees from the c-axis at a wavelength of 650 nm. The positive direction of the b axis is defined to be pointing out of the page. ........................................................................55 4.3 (Left) Commercial gemological polariscope. Example of YSO’s extinction axes observed using a polariscope, Fig (Center) viewing the crystal along the D1 or D2 axis. (Right) viewing the crystal along the b-axis shows the change in transmission because of the rotation of the dielectric axes. .........................................................................56 4.4. Diagrams showing the extremes of the transmitted color with the rotation of the crystal between crossed polarizers. The dielectric axes change as a function of wavelength relative to the crystal axes indicating the direction of the b axis. .......................57 4.5. A photograph of YSO’s birefringent pattern looking along the D2-axis using crossed polarizers and a conoscope. The horizontal b-axis and vertical D1-axis are aligned with the crossed polarizer axes. The blue and red fringes, parallel to and straddling the b-axis, show the rotation of the optical axis and plane. Note the sample shown has the crystal facets cut approximately 5 degrees off from the b and D1 axes. ....................58 5.1. (a) Energy levels of Er3+ and RHS schemes for ground and excited-state spin coherence studies (|1> ↔ |2> and |3> ↔ |4 > are electron spin transitions). (b) The RHS measurements at 3 K on Er3+ at site 1 of Y2SiO5. Lines: fitted Zeeman transition frequencies for zero-nuclear-spin Er3+ isotopes. Black circle and dashed lines: spin echo experimental condition. ................................................................................66 5.2 (a) Optically detected electron spin echoes in the 4I13=2 excited state for different pulse delays with T = 1.9 K and B = 8.7 mT. (b) Measurement (circles) and fit (line) of echo decay at 1.9 K, giving T2 =1.6 ± 0.2 μs and x=1.4 ± 0.2. Inset: rf pulse sequence. ................................................................................................................................67 xii LIST OF FIGURES CONTINUED Figure Page 5.3 (a) Excited-state stimulated spin echo decay measured at 2.5 K (circles) and fit to the spectral diffusion model (line, see text). Inset: rf pulse sequence. (b) Experimental coherence (squares) and population lifetimes (circles) as a function of temperature. Dotted line: population lifetime deduced from the sum of optical emission and excitation rates; solid lines: calculated and fitted curves (see text). .......................................67 5.4. Experimental set-up of A) the CW RHS and B) RHS spin echo measurements. C) Picture and D) diagram of the sample holder in the cryostat. ................................................73 5.5. Example of fits to the experimental A) 3-pulse and B) 2-pulse spin echo decays at several temperatures. All 2- and 3-pulse echo decays were together with shared parameters. For the sake of clarity in the figure, only a few selected decays are shown. .....................................................................................................................................77 6.1. Possible sites of Tm ions in a yttrium gallium garnet crystal. Black thick axes denote the cubic unit cell boundaries. Each of the 6 colored cuboids denotes the location as well as the direction of the ion's local Y-axis (along the cuboids largest dimension), expected to be the direction of the optical transition dipole moment of the thulium transition, relative to a cubic crystal cell. Each site is identified by a specific color throughout the remainder of this letter: "Site 1" (Black), "Site 2" (Purple), "Site 3" (Orange), "Site 4" (Yellow), "Site 5" (Green), "Site 6" (Blue). Red axes denote the symmetry axes along which the crystal is grown and oriented for these studies. Throughout this letter we will characterize rotations with respect to these directions <1-10>;<111>;<-1-1>, and rotations with respect to them. Finally, the labeled (x,y,z) thin black axes denote the local site axes as defined by the D2 point group symmetry(shown is the example of Site 1). ...........................................................................88 6.2. a. Diagram of the level structure for the optical transition in Tm169 with increasing magnetic field. Note that on a large scale the change in energy of all the spin states is dominated by the quadratic term, but for small fields it is linear. b. A detailed serrodyne scan of a spectral hole structure measured for a magnetic eld of 90 mT applied along the crystalline <111> axis. The small feature at 2 MHz is likely a spectral feature arising from the other set of sites for this orientation. c. Double passed AOM frequency scan of a broader spectral hole at 300mT. Only Δg-Δe anti- holes are visible for a pair of differently oriented sites. d. Markers show the anti-hole frequencies plotted vs the angle between the external magnetic field and the crystal's <111> axis. Solid lines of each color are fits of a "difference" tensor to each of the six potential sites for the ions with a coefficient of determination R2 > 90%. .......................89 xiii LIST OF FIGURES CONTINUED Figure Page 6.3. a. Diagrammatic view of the ODNMR experiment, including the driven spin transition that appears at small magnetic elds, and the coherent RF drive that equalizes the population between the ± 1/2 spin states. b. The ωRF frequencies that diminish the height of a spectral hole are identified as resonances by a smoothing and peak finding algorithm and then confirmed manually. A spectrum such as this one is generated for many angles between the field with the crystal || < 211 > axis. c. A plot of resonances from all spectrums at a series of angles between external eld and the crystal < 211 > direction. d,e,f Site by site fitting of the tensors listed in I to the resonances from c across a series of angles. .....................................................................90 6.4. a. The linear splitting of the anti-holes shown in Fig.2 b. for the B ||<111> orientation yields values of 45 &108 ± 2 MHz/T and a side hole splitting of 63 ± 2 MHz/T. b. Absolute absorption frequency for the optical transitions from the lowest ground state crystal eld level to the first (795.325 nm) and second (793.7nm) excited state crystal field levels with increasing magnetic field. c. A closer look at the behavior of these transitions reveals the expected quadratic nature of the frequency shift. ......................92 6.5. a. The shift in the optical transition frequency follows a quadratic dependence with an extrema that, for every orientation, appears at a positive eld for the spin conserving -1/2→-1/2 transition (blue) and at some negative eld for the spin conserving +1/2→+1/2 transitions (red). b. For the -1/2→-1/2 spin conserving optical transition and for all angles, the magnetic eld value of this extrema is identified. c. Angular gradient of the optical transition frequency at a eld of 19mT. Two points are visible for which the angular gradient gets approaches zero. d. Energy shifts of the two -1/2 spin states at this particular direction vs. magnetic eld magnitude. At 19mT the slope of the energy change for both states with change in eld magnitude is equal (along with the other derivatives) and an optical clock transition occurs......................................................................................................................93 6.6. Secondary SHB directional fit. a. Spectral hole burning anti hole splittings measured for an optical axis along the crystalline <110> axis. Dotted line indicate the minimum measurable splitting due to the width of the central spectral hole. ........................97 6.7. Secondary ODNMR directional fit using ODNMR data. a. All ODNMR resonances measured for an optical axis along the crystalline <110> axis. b,c,d. Site by site fitting of the tensors listed in the main text to the resonances from a across a series of angles. .....................................................................................................................................98 6.8. a-f. Site by site orientation map of the ground state splittings. The highlighted extrema of each surface indicate the orientations of improved sensitivity to angular magnetic field fluctuations. ....................................................................................................98 xiv LIST OF FIGURES CONTINUED Figure Page 6.9. a-f. Site by site orientation map of the branching ratio R as defined in [6]. Each site reaches a maximum branching ratio of 5% for certain angles close to the particular local x axis ..............................................................................................................................99 7.1. Energy-level diagram for 171Yb3+:YVO4. (a) Crystal-field splittings of 171Yb3+:YVO4 reproduced from [51]. (b) Zero-field energy level diagram for the 2F 2 7/2(0) → F5/2(0) transition of 171Yb3+:YVO4 at 984.5 nm studied in this paper. Energy splittings in the ground and excited state are extracted from the excited-state hyperfine tensor determined in this work and previous measurements of the ground-statehyperfine tensor [154]. The transitions corresponding to the observed absorption spectrum in Fig. 7.2 for E || c (E ⊥ c) are shown in solid blue (dashed red). The dotted grey lines correspond to transitions that are forbidden by symmetry. (c) Energy-level diagram for the linear Zeeman regime with B || c with arrows denoting the transitions studied in this work. ..........................................................................................................................106 7.2. Optical-absorption spectra of the 2F → 2F transition of 171Yb3+ 7/2(0) 5/2(0) :YVO4 at 2 K and zero applied magnetic field for light polarized parallel (solid blue) and perpendicular (dashed red) to the crystal c axis. ..................................................................107 7.3. (a) Typical high-resolution absorption spectra for a magnetic field ramp with B,k ⊥ c and E ⊥ c showing resolved optical hyperfine transitions. Darker regions correspond to higher absorption. (b) Simulated absorption spectra using the experimentally determined spin Hamiltonian for magnetic field ramp with B,k ⊥ c and E ⊥ c. The simulated absorption spectra take into account a slight misalignment (∼1◦) between the crystal a axis and the applied magnetic field. .................................................................108 7.4. Excited-state lifetime measurement via fluorescence decay. An exponential fit (dashed line) gives τf = 267 ± 1 μs. .....................................................................................109 7.5. (a) Typical photon echo decays for B || c showing an increase of coherence time and strong nonexponential decays with increasing magnetic field. Fits to a Mims decay are shown for each field value as a solid line (see main text for details). (b) Effective linewidth extracted from the fits to the photon echo decays for B || c. ................................110 7.6. Continuous-wave Raman heterodyne measurement of the nuclear-spin inhomogeneity with B = 440 mT parallel to the c axis. A Lorentzian fit gives a FWHM of 250 kHz. ..............................................................................................................110 7.7. Typical nuclear-spin echo decays for increasing applied magnetic field along the c axis. The echo sequence is performed with direct microwave excitation and read out optically. .........................................................................................................................110 7.8. Typical nuclear-spin-echo decays for increasing magnetic fields applied 20◦ from the c axis. Here, the entire sequence is performed using all-optical manipulation of the spins. .....................................................................................................................................111 xv LIST OF FIGURES CONTINUED Figure Page 8.1. Fluorescence decay and decay of spectral hole area of the 4I13/2 (Y1) excited state. Both experimental data sets are fit to an exponential decay to extract the levels lifetime ..................................................................................................................................118 8.2. Absorption spectrum of the 4I 4 15/2(Z1) → I13/2 (Y1) transition in 0.1% Er:YAG and 1% Er:YAG at zero field and 3.4 K. The peak absorption coefficients are 3.5 cm-1 (0.1% Er:YAG) and 33.3 cm-1 (1% Er3+:YAG). .................................................................119 8.3. Absorption spectrum of the 4I 4 15/2(Z1) → I13/2 (Y1) transition in 0.05% Er3+:YLuAG. .........120 8.4. Observed thermal frequency shift (top) and thermal broadening (bottom) of the 4I 4 15/2(Z1)→ I13/2 (Y1) transition for 0.1% Er3+:YAG............................................................120 8.5. Diagram illustrating the relative orientation of the six magnetically inequivalent sites in YAG that are occupied by erbium ions. ...........................................................................121 8.6. Splitting of the 4I 4 15/2(Z1) → I13/2 (Y1) transition in a magnetic field. (a) Relevant energy level structure. The degeneracy of both the 4I15/2(Z1) ground and 4I13/2 (Y1) excited state is lifted by the application of a magnetic field B, leading to the appearance of 4 transitions for one site. (b) Example absorption spectrum for B = 2:5 T and T = 1:6 K. The magnetic field, as well as the light polarization were orientated along the X axis of the crystal, X corresponding to 16 deg off the [-1-12] crystalline axis by a rotation about the [1-10] axis. ...............................................................................121 8.7. Frequency shift of the eight lines observed on the 4I15/2(Z1) 4 → I13/2 (Y1) transition as a function of magnetic field strength, for B || X. Each pair of lines, corresponding to a set of spin-preserving or of cross transitions for a particular subset, is represented by one color. The experimental points are fitted by polynomial functions up to the second order (solid lines). Parameters are given in Table II. Zero shift corresponds to 1526.66 nm. ..........................................................................................................................122 8.8. Shifts of the optical transitions as a function of the magnetic field orientation for B=1T in 0.1% Er:YAG. The magnetic field was applied in the X-Y plane, where X corresponds to the crystalline axis [-1-12] rotated by 16 deg about [1-10] and Y corresponds to [1-10]. The rotation of the magnetic field was about the Z axis of the crystal, Z corresponding to the crystalline axis [111] rotated by 16 deg about [1-10], and θ = 0 corresponding to B along X. We observed various lines that we identified to originate from site 1 (blue), site 2 (red), site 3 (purple), site 4 (green), site 5 (orange) and site 6 (cyan). Experimental data were taken at 1.6 K (dots) and at 5.0 K (stars). The lines (solid for spin-preserving and dashed for cross) represent our fit, which gives us the components of the excited state g-tensor (see main text). .....................123 xvi LIST OF FIGURES CONTINUED Figure Page 8.9. Scheme of spectral hole burning with structured excited-state. First, a strong burning pulse excites ions which are on-resonance, creating a spectrally narrow hole in the absorption profile. In a second step, the frequency-scanned weak probe pulse experiences less absorption when it is on resonance with the first burning pulse, but also when it is detuned by the excited state splitting Δe, because of the lack of ions in the ground state. The later is called a sidehole. ....................................................................124 8.10. Hole burning spectra exhibiting sideholes at the excited state splitting for magnetic fields between 0 and 10 mT and for 3 orientations: (a) B||Y , (b) B || Z, and (c) B || X in 0.1% Er:YAG. The experimental data are shown together with the theoretical position of the sideholes, predicted by the excited state g-tensor obtained by the orientation dependence fit, after applying a correction rotation of the magnetic field orientation of less than 10 degrees. ......................................................................................124 8.11. Example of a typical two pulse photon echo decay at B = 6 T and T = 1:6 K. ..................125 8.12. a) Magnetic field dependence of the effective homogeneous linewidth, b) temperature dependence of the effective homogeneous linewidth. .................................125 8.13. (a) Magnetic field and (b) temperature dependence of the spectral diffusion rate (see Eq. 6). ...................................................................................................................................125 8.14. Orientation dependence of the measured homogeneous linewidth at a field of 2 T and 1.6 K for fields in the Y -Z plane (relative to B||Z at zero degrees) . Error bars are smaller than the size of the data points. ..........................................................................126 8.15. Spectral diffusion measurements on line 2 of the 4I15/2(Z1) 4 → I13/2 (Y1) transition using three-pulse photon echoes. a) Homogeneous linewidth as a function of t23 for various B fields. b) Dependence of the spectral diffusion rate R on the B field, fitted using Eq. (6). c) Dependence of the spectral diffusion linewidth ΓSD on the B field, fitted using Eq. (5). ...............................................................................................................127 9.1. (a) Level structure of Tm:YAG without and with an applied magnetic field. (b) Hole burning spectrum of the 1% Tm:YAG bulk crystal together with a fit (red line). ...............134 9.2. XRD spectra of selected powders together with the reference spectrum (JCPDS # 30- 0040) of YAG. (a) Chemical synthesis; (b) Crytur non-annealed; (c) SMC low energy ball milled; (d) SMC low energy ball milled and annealed. .....................................135 9.3. SEM images and typical hole burning spectra of the powder obtained after ball- milling the bulk crystal from SMC for two days. (a), (c) before, and (b), (d) after annealing at 1400◦C for 4 h. .................................................................................................136 9.4. (a) SEM image of the 1% Tm:YAG powder provided by Crytur, and typical hole burning spectrum (b) before and (c) after annealing. ...........................................................137 xvii LIST OF FIGURES CONTINUED Figure Page 9.5. SEM image of the 1% Tm:YAG powder after 4 h of high-energy planetary ball- milling...................................................................................................................................137 9.6. SEM image of the synthesized 1% Tm:YAG powder. .........................................................138 10.1. Scanning electron microscope images of (a) powder #1 made from a 0.1% Er3+:LiNbO3 bulk crystal (SMC) by grinding with a mortar and pestle,(b)powder #2 ball-milled for only 30 min...................................................................................................146 10.2. Scanning electron microscope images (a) powder #3 ball-milled and annealed at 900 C, and (b) powder #6 annealed up to 1100 C. ...............................................................147 10.3. (a) Orientation dependence of the effective linewidth Γeff in a 0.1% Er3+:LiNbO3 bulk crystal measured at T=1.6K and B=2 T. The magnetic field orientation is rotated by an angle θ from the c-axis of the crystal. The inset shows an example echo intensity decay at θ = 0 i.e. B∥c, where the fit of Eq. (1) gives Γeff = 1/πTM = 3.1kHz. The red solid line is an empirical polynomial fit to the experimental Γeff (θ) data. (b) Decay of the echo area for the 0.1% Er3+:LiNbO3 reference powder. The dashed line corresponds to a fit of a sum of two exponential decays to the experimental data(black dots). The red solid line corresponds to a calculation of the expected decay in the powder due to the orientation dependence of Γeff in the bulk crystal. .............148 10.4. Magnetic field dependence of the effective homogeneous linewidth in 0.1% Er3+:LiNbO3 at T=3 K for the bulk crystal (for B∥c), the reference powder #1,and a powder ball-milled for 30 min (powder #2). ........................................................................149 10.5. Hole burning spectrum in 0.1% Er3+:LiNbO3 (powder #1) at T=1.6K and B=2 T. Zero detuning corresponds to 1531.882 nm in vacuum. ......................................................150 10.6. Typical background-subtracted FID decay of the reference powder #1at B=3.9 T, T=1.6K and waiting time tw = 5 μs. Solid points are measured values and the solid line is a fit of the FID signal. The inset shows a magnification of the first 1 μs of the decay. ....................................................................................................................................152 10.7. Effective homogeneous linewidths at (a) B=2 T and (b) B=3.9 T at T=1.6K as a function of the waiting time Tw measured using the delayed FID technique for powders #1, #3 through #6 and for the bulk crystal. The solid lines are guides to the eye.........................................................................................................................................119 11.1. Relevant energy levels of Tb3+:Y3Al5O12(vertical axis not to scale) for measurement of the population relaxation between the first two crystal-field levels within the 5D4 excited-state manifold. A pulsed laser excited the ions from the 7F6 a ground state to the 5D4 f excited state, from where they decay rapidly into 5D4 a and b. The resulting fluorescence due to the four 5D4 a/b →7F5 a/b transitions was collected, spectrally resolved, and then analyzed. Inset: Relaxation processes (nonradiative, red; radiative, green) for populations on the two excited levels 5D4 a/b (see definitions in the text). ........159 xviii LIST OF FIGURES CONTINUED Figure Page 11.2. Fluorescence spectra at 5 K of (a) a 40-nm-diameter powder and (b) a 500-nm- diameter powder (synthesized via method 1).Each spectrum (black circles)was fitted by the sum of four identical Lorentzian lines with the same pairwise energy splitting Δ (Δ’). For d = 40 nm the width is 53 GHz and Δ is 40 GHz, and for d = 500 nm the width is 13 GHz and Δ’ is 39 GHz. ......................................................................................160 11.3. Fluorescence decays 5D4 a/b → 7F5 a/b at 1.5 K in large crystallites (d = 500 nm). The experimental points were fitted by Eq. (9) (solid lines), resulting in γa = 237±0.5 Hz and γba = 3.36 ± 0.03 kHz. Inset: Magnification of the first 2 ms of the decay. .................................................................................................................160 11.4. Fraction of particles suppressing phonons β obtained from an average of the fits of Eq. (9) to the four decays 5D4 a, b → 7F5 a, b as a function of the average nanocrystal diameter d for powder 1 (red) and powder 2 (blue) at 1.5 K. Simulations are depicted using dashed lines. Inset: Characteristic time of the fast decay component as a function of the nanocrystal diameter d. ......................................................161 11.5. Ratio of population nb/na as a function of temperature in the bulk crystal (black squares) and in nanocrystals from method 1 of average diameter d = 72 nm (red triangles) and d = 40 nm (blue circles). Solid lines are best fits using Eq. (3), and shaded areas represent uncertainties. ....................................................................................162 11.6. Microscope images of 1% Tb3+:Y3Al5O12 created using method 1 and annealing at 1400 C (a) or 900 C (b, c) and using method 2 and annealing at 900 C (d). (a, b, d) SEM images, showing the size distribution of the nanocrystals. (e, f)XRD spectra of powders produced by methods 1 and 2, respectively (solid blue lines), and the corresponding reference spectrum (JCPDS No. 30-0040; red circles) for YAG. (c) High-resolution TEM image showing the crystalline structure (narrow white lines), which can extend over several particles if they are agglomerated. ......................................163 11.7. Particle-size (d) dependence of the radiative lifetime of the 5D4 a level for powders from method 1 (red circles) and powders from method 2 (blue squares). The solid line shows the expected dependence. ...................................................................................164 11.8. Particle-size dependence of the inhomogeneous line width for powders from method 1 (red circles) and powders from method 2 (blue squares). Inset: Splitting Δ between the 5D4 a/b levels versus particle size. Solid lines are guides for the eye. .............164 xix LIST OF FIGURES CONTINUED Figure Page 11.9. Ratio n2/n1 of populations in the ground manifold 7F6 b/a levels as a function of the temperature Tset read by the cryostat sensor for a bulk crystal (black circles) and nanocrystalline powder samples with diameters d = 124 ± 30 nm, produced by method 1 (blue squares), and d = 63 ± 11 nm, produced by method 2 (red triangles). The solid line is the fit to a Boltzmann distribution with Δg = 83.5 GHz. Note that the large error bar for 3.2 K and d = 124 nm is caused by the large uncertainty of the fit to that particular absorption spectrum. .................................................................................165 12.1. The ray tracing and momentum changes due to propagation of a laser beam with a strong intensity gradient of radius smaller than the particle diameter. The figure is similar that of Ashkin’s original paper. The combination of the change in momentum per photon and the transverse gradient of the laser beam results in two net forces: a gradient force towards the beam axis and a scattering force in the direction of the laser beam’s propagation. .....................................................................................................170 12.2. Two counter-propagating focused laser beams for an optical trap. ....................................171 12.3. The average chamber pressure when 3 micron spherical particles are lost as a function of laser intensity. Each point represents the average loss pressure for 5 trapped particles at a given intensity. ...................................................................................171 12.4. Basic concept of solid-state (anti-Stokes) laser cooling. The absorbed light from a thermally excited ground state level to the lowest excited state level and subsequent emission from a thermally excited state level to a lower ground state level results in a net loss in energy from the material. ....................................................................................172 12.5. Imaging of Yb3+-doped YAG crystals under laser excitation traveling down the center of the rod. a) Yb3+:YAG single crystal rod (1 mm diameter) under laser excitation by 200 mW of non-resonant laser light at 1040 nm as seen through a ~950nm filter. Minimal fluorescence is observed. b) Observation of ~950 nm anti- Stokes fluorescence from Yb3+ ions as laser is tuned near resonance at 1030 nm. c) Strong anti-Stokes emission observed when laser is tuned to peak of resonance at 1030 nm. d) Thermal image of crystal with 200 mW of on-resonance 1030 nm laser light, demonstrating no significant heating of crystal relative to ambient temperature (74°F) even when laser light is strongly absorbed. ..............................................................173 12.6. Top Left: 3240x Magnification Yb:YAG, Scale 10um. Top Right: 18560x Magnification Yb:YAG, Scale 2um. Bottom Left: 21560x Magnification Yb:YAG, Scale 1um. Bottom Right: 49310x Magnification Yb:YAG #1, Scale 200nm. ...................173 xx LIST OF FIGURES CONTINUED Figure Page 12.7. Examples of spherical particles of birefringent vaterite crystals (CaCO3) fabricated at MSU. Left: Typical microspheres produced with sizes in the 1 to 10 micron size range. Middle: Example of larger ~30 micron diameter vaterite microsphere produced by increasing growth time. Right: Example fluorescence image of rare- earth-doped vaterite particles produced with Eu3+ ions used as the fluorescence marker, demonstrating the ability to dope the vaterite microspheres with rare-earth ions. ......................................................................................................................................173 12.8. Left: Optical thermometry setup Right: Results from fluorescence thermometry experiment showing a linear relationship of the fluorescence ratio at high temperature. ..........................................................................................................................174 12.9. Left: Launcher with reservoir and small drop hole. Middle and right: Launcher with reservoir and trenched channel. ............................................................................................175 12.10. A schematic of our horizontal dual-beam optical trap for trapping microspheres in air and vacuum. A single 1030 nm laser beam is split into two counter-propagating beams (B1 and B2) with a polarizing beam splitter (PBS) and balanced in power with a Babinet-compensator (BC). The beams enter the vacuum chamber and each pass through an 8 mm aspheric lens. The component library from gwoptics was used to create this diagram............................................................................................................175 12.11. Trapped soda lime glass microsphere (5-25 micron diameters) in horizontal dual- beam optical trap. .................................................................................................................176 xxi ABSTRACT High-quality rare-earth-ion (REI) doped materials are a prerequisite for many applications such as quantum memories, ultra-high-resolution photonic signal processing, and quantum-limited sensing. Realization of practical solid-state photonic technologies critically depends on finding materials that offer necessary combinations of optical and spin-state coherence, spectral multiplexing capacity, transition wavelengths, and many other key properties. To realize these advances, we continue to improve the fundamental understanding and control of physical processes that govern ion-ion, ion-spin, and ion-lattice interactions. Furthermore, exploring the role of material chemistry and fabrication in determining the observed properties is crucial. With these motivations, we study a range of rare-earth-doped optical materials using powders and single crystals to understand and optimize the properties relevant to quantum memory, quantum transduction, photonic signal processing, and optical cooling applications. In addition to producing, measuring, and analysing spectroscopic and coherence properties of promising material systems, we highlight the engineering of lattice defects to manipulate both static and dynamic disorder. This work spans nine different REI doped materials: four single crystals, Tm3+:Y3Ga5O12, Yb3+:YVO4, Er3+:Y3Al5O , and Er3+ 12 :Y2SiO5, and five crystalline powders, Er3+:LiNbO3, Tm3+:Y3Al 3+ 5O12, Tb :Y3Al5O12, Yb3+:YAG, and Eu3+:CaCO3. These choices are based on material properties unique to each system, need for investigation, or potential for systematic comparison of fabrication methods and stoichiometry. Spectral hole burning (SHB), optical and spin coherence measurement techniques are sensitive quantitative characterization tools, complementing traditional optical, chemical, and structural analysis. We find that coherence and spin lifetimes are especially sensitive to low levels of strain and defects in the crystal, undetected by other methods. Properties of REI doped materials are found to vary by orders of magnitude depending on the source, synthesis, and implementation of the materials. Even mild mechanical processing producing large variations in spin lifetimes and SHB properties. These variations are attributed to low levels of glass-like dynamics in the crystalline lattice introduced by inhomogeneous strain and chemical defects, which can be reduced or eliminated by annealing or improved fabrication. Overall, these studies reveal that SHB or coherence measurements are needed to identify material dynamics and guide the fabrication process to reach the true fundamental capabilities of REI materials. 1 CHAPTER 1 INTRODUCTION TO RARE EARTH IONS Background of Rare Earth Ions in Solid State Materials Rare earth ions doped into solid-state crystalline materials are used for fundamental research and commercial technologies because they have the most complex and useful spectra of all the known elements [1-3]. The rare earth ion’s visible and infrared spectra are due to the fourteen possible electrons in the 4fN shell and the energy transitions within the 4fN shell. Using the resonant wavelengths of these intra-configuration transitions, the rare-earth-ion (REI) doped materials can be used for new optical technologies [4-9]. Some of these optical systems include laser frequency narrowing and stabilization [10-15], high-bandwidth optical signal processing [16-19], optical filtering for medical imaging technology [20-22], and optical memory systems [6,9,10,23-25]. The REIs can transfer and store quanta of information while preserving the frequency and phase coherently; thus, they are ideal for proof of concept and scaling quantum architectures such as quantum transducers and quantum memories [11,23-33]. Commercial applications built using REI doped materials are important in a wide range of industries. These include neodymium and ytterbium high powered lasers for manufacturing and machining, erbium optical amplifiers for global broadband communications, as well as europium and thulium phosphors used in an ever-growing number of visible optical applications. The focus of this work is developing new and current REI doped materials for optical applications. Understanding how the materials are produced, their fundamental physical and 2 optical properties, and the needs of the applications, we can utilize the entire process of growing crystals and the optical technologies using them from the ground up. The 4fN Electrons of Rare Earth Ions The lanthanide elements doped into insulators are generally trivalent ions, giving up two electrons from the outermost electron orbital shell and one from the 4fN orbital shell. The radial orbit extent of the remaining 5s, 5p, and 6s electrons extend beyond the 4f orbital shell. These outer electrons of the REIs participate in the chemical bonding with the surrounding crystal ions or ligands. Unlike the 3dN, 4dN, 5dN orbitals of transitions metals, the 4fN electron shell is effectively shielded from the host’s materials bonding forces, minimizing significant changes to the 4fN shell. The central field radial contribution of the Hamiltonian, which can be modeled as spherically symmetric, separates the electron configurations but does not remove the degeneracy of the 4fN configuration. The major contributions to the 4fN electronic energy level structure are the inter-electronic repulsion and the spin-orbit coupling. The inter-electronic repulsion separates levels by 104 cm-1, and the spin-orbit coupling has energy levels on the order of 103 cm-1. An effective Hamiltonian term describing the crystal environment, the “crystal field,” makes the smallest nominal contribution, typically around 102 cm-1. The hierarchy of these contributions is shown in Figure 1.1. 3 Figure 1.1. Illustration of the interactions affecting the energy levels of 4fN configurations in lanthanide ions. The partially filled 4fN electron orbitals of the rare earth ions provide unique optical properties. The REI’s optical transitions are between the 4fN-4fN states, which are nominally forbidden quantum transitions. However, these transitions are weakly allowed due to the crystal field breaking the symmetry by adding small admixtures of opposite parity electron configurations. This “forced” electric-dipole character of the transition makes the transition probability low, and thus the oscillator strengths are weak, allowing long excited state lifetimes. Since the 4fN electrons are shielded inside the bonding electrons, unlike transition metals, the rare earth ion 4fN-4fN transitions have weaker electron-phonon coupling. The REIs can have very narrow linewidths at liquid helium temperatures, which can provide large peak absorption coefficients despite the weak oscillator strength. 4 Narrow optical transitions occur throughout the spectrum from the infrared to the ultraviolet. Since the larger scale energy structure of the f-f transitions primarily arises from the ion’s internal electronic structure and is weakly dependent on the material, the transitions in the crystal are similar in all host materials. This property allows photonic components to be designed around a particular REI transition. While many different host materials are available the details of the transitions must be measured. A universal diagram thus can be made for REI energy levels independent of host materials. Known as the Dieke diagram, in honor of Wilhelm Dieke who directed extensive measurements of the optical transitions for each trivalent rare earth ion [1]. When choosing and identifying rare earth transitions in new materials the nominal labeling of the major 2S+1LJ manifolds is used as seen in Figure 1.2, where S is the total spin angular momentum, L is the total orbital angular momentum, and J is the total angular momentum. The REI’s require intermediate coupling, so the L and S in the REI term symbols are not good quantum numbers. The total angular momentum J is a good quantum number, and the number of crystal field levels is equal to 2J + 1. Where the odd electron ions with half integer spin will have double degenerate crystal field levels which can be split by a magnetic field. The lowest energy transitions between J-multiplets are of the greatest interest for spectral hole burning applications. The energy gap between the lowest level of the J-multiplet or the next lowest energy manifold needs to be large compared to the phonon energies. That ensured that the excited ions primarily relax by optical radiative emission to the lower states. The higher energy states of each J-manifold are more homogeneously broadened due to rapid non-radiative relaxation to lower states. - 250 - 250 - 275 - 275 - 299 - 299 5 - 334 - 334 Figure 1.2. Dieke Diagram showing energy levels of the trivalent rare earth ions erbium, thulium and ytterbium. The red arrows signal the transitions in use in this thesis. The diagram is scaled in wavenumbers and wavelength and the visible spectrum, which is marked in color. Resonant Linewidths of REI in Crystals At room temperature, phonons are the largest contribution to the linewidth, producing homogeneously broadened spectral lines. Cooling the crystal below 10 K will suppress the dynamics phonon perturbations, and the homogeneous lines can become extremely narrow. Therefore, optical and spin properties of rare earth ions are studied at cryogenic temperatures. Wavenumbers (x1,000 cm-1) Wavenumbers (x1,000 cm-1) 6 The crystalline environment of a resonant ion varies from site to site within a single crystal; thus, the ions experience different local transitions due to strain, caused by crystal imperfections, impurities, or defects. The static strain variation at each site slightly shifts the center of the transition frequency, and at low temperature, the spectral lines of rare earth activated materials are inhomogeneously broadened [10]. The REI can have millions of homogeneous lines under the inhomogeneous absorption packet, where each line is an ensemble of ions, in different spatial locations, which are excited at the same frequency. The ensembles can be used to store wavelength and amplitude information as well as phase and temporal information. The homogeneous linewidth, Γh, is nominally the same full width at half max energy width for each resonant ion in the material and ideally has a Lorentzian line shape. The dynamic perturbations to the transition frequency or phase due to various mechanisms, combine to broaden the homogeneous linewidth and disrupt the transition’s coherence. These mechanisms include phonon scattering, electronic or nuclear spin flips, dynamic disorder, or other low energy mechanisms allowing the REI to fluctuate between similar energy states [4]. The linewidth and shape can be used as a direct measure of the static and dynamic disorder in the material, providing information on the defects responsible for the broadening [34]. The inhomogeneous linewidth, Γinh, of REI activated single crystal materials can vary in scale. For example, Er3+:Y2SiO5 has an Γinh = 500 MHz while Tm:YGG has an Γinh = 56 GHz. Thus, there can be as many as 108 homogeneous lines within the inhomogeneous line for single crystal materials [24]. 7 All these properties combine to make rare earth activated materials very useful in photonic technologies. However, choosing and finding the ideal crystal for an application is not always straightforward. Knowledge of the fundamental properties helps inform which material should be pursued next. Outline of Dissertation A range of rare earth ion doped materials are used to understand how the optical and quantum properties change between REIs and host materials. This study focuses on characterizing and fabricating optical materials for fundamental science and innovative technologies. In Chapter 2, an overview of the fabrication is given for the materials used. The motivation for each material is described, with an insight into why the REI and host combination was chosen. Chapter 3 reviews the characterization and equipment for each spectroscopy method used and summarizes other characterization techniques used for both the powders and single crystals. The orientation of an anisotropic sample such as the biaxial Y2SiO5 is especially important. Therefore, the crystallographic orientation of birefringent materials is simple, quick, and effective using crossed polarizers in Chapter 4. Then each chapter focuses on a specific material studied. In Chapter 5, the electron spin coherence of Er:Y2SiO5 is used to demonstrate microwave to optical quantum transduction [33]. In Chapter 6, the Tm:Y3Ga5O12 system g-tensor is characterized with a full rotational analysis in a magnetic field to study how linewidths and coherence properties are affected. In Chapter 7, the Yb:YVO4 crystal is characterized for quantum applications and found to be an ideal candidate for the 980 nm ytterbium transition with narrow inhomogeneous and homogenous linewidths ideal for new quantum applications [35]. In 8 Chapter 8, the Er:Y3Al5O12 crystal is characterized for photonic applications, measuring the linear and quadratic Zeeman shifts and orientation dependance, and the coherence time are measured as a function of magnetic field and temperature to study the decoherence mechanisms of the 1527 nm erbium transition. REI doped crystal powders are pursued in Chapters 9, 10, 11, and 12 to determine if powders can be used in place of a single crystal for optical technologies. The REI powders were fabricated and characterized to find how different processing influenced the material’s optical and coherence properties. In Chapter 9, the Tm:Y3Al5O12 spin relaxation properties were used to characterize the powder fabrication process [36]. In Chapter 10, The mechanical processing and annealing of Er:LiNbO3 powder is studied [37]. In Chapter 11, the relaxation dynamics of Tb:YAG are altered through different fabrication techniques [38]. Chapter 12 explores optically levitated particles and solid-state laser cooling for quantum limited optical sensors. Finally, a closing perspective on the materials used in this thesis and concluding remarks are given in Chapter 13. 9 CHAPTER 2 RARE EARTH ION DOPED MATERIAL PROPERTIES AND SYNTHESIS Survey of Materials Studied The Cone/Thiel group has a long history of studying materials for quantum and classical information processing. Many materials are characterized in the quest to find the ideal material. Ideally, the spectral properties of every crystal that can incorporate a rare earth ion would be characterized. At least 500 single crystals have been identified to be useful as a laser material and there are many more that may be useful for new technologies [39,40]. Therefore, a few selected high-quality single crystal materials and powders produced and compared to the bulk crystal are studied in detail. All the crystal materials used are insulating dielectric inorganic oxides doped with REIs at suitable concentrations. The materials include Y3Al5O12, Y3Ga5O12, Y2SiO5, YVO4 and LiNbO3. Obtaining high-quality single crystal samples of these materials can be difficult, so it has been to our advantage that the Cone/Thiel group has collaborated with Scientific Materials since they started growing crystal in Bozeman in 1989. The quality of the crystal can significantly influence the properties of the material, which are especially pronounced when the optical and electron spin coherence of the REI material are measured. The chemical properties, dopant levels, symmetry, orientation, and other physical properties along with material production, should all be considered. The materials chosen all have the essential crystal properties needed for laboratory and industrial use. The requirements include several factors such as, chemical inertness and stability at standard temperatures and 10 atmospheres, hardness, and fabrication considerations such as toxicity, melting point, the feasibility of growth, cleavage planes, availability of material and an operational transparency range around the REI transition of interest [42]. Low defect and inclusion density is wanted to minimize scattering for high clarity. Choosing host materials with low or zero nuclear spin atoms can reduce decoherence mechanisms in the REI [41,43]. Single crystals are more easily grown into large boules if they have uniform thermal properties; specifically, higher thermal conductivity and lower thermal expansion coefficients are desirable and are especially beneficial for high-power laser materials. Hardness, chemical, and atmosphere stability allow more uniform, longer lasting polished optical surfaces. Powders of crystalline material are of interest because many devices are miniaturized, and the powders can give insight into how a REI material will perform when scaled down. Materials properties such as size and shape that could not be investigated as single crystals can also be characterized. Powders also open the possibility to survey a larger number of material iterations without the cost of growing single crystal boules. There are hundreds of REI transitions across the series; therefore, the best transitions will depend on the research or application of interest. The REI will have long lifetimes and long coherence times; thus, the transition will not have energy levels close enough together that the ion can relax through phonons or non-radiative transitions. A transition that is resonant with commercially available laser technology is also a great advantage in technology. Each REI material has distinct differences and advantages, therefore, the motivation and the details of the transition for the REI used in each study are discussed. 11 Rare Earth Doped Single Crystals The single crystals studied here are Er3+:Y2SiO5 (Er:YSO), Tm3+:Y3Ga5O12 (Tm:YGG), and Yb3+:YVO4 (Yb:YVO), along with the single crystals compared to the powders, Er3+:LiNbO (Er:LN), Tm3+ 3 :Y3Al5O12,(Tm:YAG), and Tb3+:Y3Al5O12 (Tb:YAG). Both single crystals and powders were studied to find materials for quantum information systems. However, often it was found that the single crystals have superior optical and coherent properties compared to the powders. Thus, they are generally preferred over powders and often needed to compare against for high resolution spectroscopy research. All single crystals were grown using the Czochralski growth technique, which has advantages over powders, include longer absorption paths; they can be oriented, faceted, and polished. However they are more expensive to synthesize and fabricate. Er3+:Y2SiO5 The motivation to use erbium doped yttrium orthosilicate, Er3+:Y2SiO5, (Er:YSO), started with a collaboration between the Cone Lab and Scientific Materials when the first photon echoes were observed in Er:YSO [45,46]. Erbium doped into the YSO crystal is attractive because the 4I 4 15/2↔ I13/2 transition has a radiative excited state lifetime of 10 ms. A series of Er:YSO growths enabled the crystal’s quantum properties to be engineered to produce the narrowest optical linewidth of any solid state material, 75 Hz. These groundbreaking studies have influenced research groups worldwide to study many REIs in the YSO crystal [107,118]. The study here began with an international collaboration between the Cone/Thiel group and the Goldner group in Paris, France. The goal was to develop an understanding of how the spin coherence properties of YSO could be influenced by introducing disorder to the crystal. 12 New YSO growths with a range of REI and other dopants including calcium were produced by the Goldner group and brought to Bozeman by Sacha Wilinski to study. This collaboration demonstrated that Er:YSO is an ideal material for transferring quantum information between microwave frequencies and optical frequencies. The crystal chosen for the experiments was 0.005% Er:YSO (#6-429) grown by Scientific Materials. This particular crystal was used because only 50 ppm of the natural abundance of erbium isotopes erbium was doped into the crystal allowing the Er167 zero nuclear spin isotope’s electron spin transitions to be measured with little interference. Y2SiO5 is also a low nuclear spin host, which significantly decreases the decoherence of the erbium ions. Where yttrium only has spin of ½ in the single stable isotope, and the major natural abundance of silicon and oxygen have 0 spin. . The YSO unit cell’s space group is C2/c, No. 15, with 64 atoms, consisting of 8 formula units [47]. The rare earths substitute into the two spatially and symmetrically different Y3+ sites. Both sites have the lowest C1 symmetry but are surrounded by a different number of oxygen ions. There are two magnetically inequivalent subgroups for each site [48]. We built custom RF waveguide holders to measure the electron spin lifetimes and the spin coherence as seen in the supplementary material in Chapter 5. A magnetic field can split the optical transitions of erbium to be in resonance with a microwave signal. As a result, the quantum efficiency in transferring photons from microwave to optical is nearly 100%. Furthermore, the optically excited-state electron spin coherence properties were found to be ideal since the excited state population can be controlled and the decoherence of the spin flip flops are minimized [33]. 13 Tm3+:Y3Ga5O12 The thulium doped yttrium gallium garnet, Tm3+Y3Ga5O12 (Tm:YGG), is a material being used in emerging photonic technologies such as signal processing and quantum memories in quantum information applications. Ensembles of Tm3+ ions in YGG are ideal for high- bandwidth quantum memories because the material has long coherence times up to hundreds of µs and the narrowest homogeneous linewidths of any thulium doped material known today [25- 27,49]. The Tm3+ ion has three J-multiplets absorbing in the near infrared. The ground state is the 3H6. The absorption around 1750 nm is to the 3F4, that at 1200 nm is to 3H5, and that at 795 nm is to 3H4. The 3H6↔ 3H4 transition in Tm:YGG is centered at 795.325 nm (vacuum) with a 56 GHz inhomogeneous linewidth and an absorption coefficient of 0.4 cm−1 for a 1% Tm concentration [49]. The index of refraction of YGG is 1.95 at 795 nm [179]. The absorption coefficient is relatively weak [25] with an oscillator strength of about 18 x 10-9, smaller than other Tm3+ doped materials [24]. The yttrium gallium garnet, YGG, is a direct analog to the yttrium aluminum garnet, YAG, substituting gallium for aluminum. They are chemically resistant and non-hygroscopic, have a high optical damage threshold, and incorporate rare earth ions into the yttrium sites. Both YGG and YAG crystals can be produced using the Czochralski technique for high quality optical oxide materials. Gallium garnets have a body centered cubic structure, space group Ia3D (O10 H, # 230), with formula units A3B2C3O12, where the A is the dodecahedral site, B is the octahedral site, and C is the tetrahedral site, all trivalent cations. The O is the O2- divalent oxygen anion in an octahedral site. A unit cell of the yttrium gallium garnet contains; 24 yttrium, 40 gallium, and 96 oxygen atoms, consisting of eight Y3Ga5O12 formula units, totaling 160 atoms in a cell [174]. 14 The cubic symmetry requires the dielectric constants to be isotropic. Therefore, there is no optical axis or piezo properties that can be used to find the orientation. Laue X-ray photographs are most commonly used to determine the crystal axes. The increased static strain due to the gallium substituted for the aluminum makes Tm:YGG’s inhomogeneous linewidth more than three times as wide as Tm:YAG. Making Tm:YGG ideal for extreme bandwidth RF spectrum analyzers or wide bandwidth photonic memories. Scientific Materials/FLIR has produced over ten separate crystal growths of Tm:YGG to be investigated as the core component of a photonic signal processing systems in a collaboration between the Cone/Thiel group and S2 Corporation [17-20]. A collaboration with the quantum information group at the Delft University of Technology also produced a study on Tm:YGG. Jake Davidson spent a few months at MSU mapping out the thulium ion spin-Hamiltonian in YGG using a combination of spectral hole burning, absorption spectroscopy, and optically detected nuclear magnetic resonance techniques. Chapter 9 shows different orientations of the Tm:YGG crystal in an external magnetic field that can extend the optical coherence times and or narrow spin inhomogeneous linewidths or improve optical pumping by mixing spin states. Yb3+:YVO4 The Yb3+ ion is an attractive choice when surveying REI materials for new technologies because the single 4fN excited state manifold of the trivalent ytterbium ion is at 980 nm, where many optical components are commercially available, including single-mode laser diodes. The Yb3+ doped yttrium vanadate (Yb:YVO4) crystal itself has an extremely high oscillator strength making it very interesting for quantum information [50, 51]. In addition, the YVO4 material is a 15 relatively low nuclear spin host allowing for less decoherence in a paramagnetic ion, such as Yb3+ or Er3+, with an odd number of electrons, also known as a Kramers ion. These properties and the fact that fabrication techniques for nanoscale devices were recently developed for quantum resonators using YVO4 as a host [52] make Yb3+:YVO4 a promising material for next- generation technologies. The Yb:YVO4 was surveyed for the energy level structure, the oscillator strengths, and the coherence of the optical and spin transitions using high resolution spectroscopy. The high absorption coefficient was measured using a crystal polished down to 90 µm to ensure the material was not over absorbed. An external cavity diode laser was used to excite and scan across the optical absorptions revealing the underlying hyperfine transitions. YVO4 has excellent thermal, chemical, mechanical, and optical properties for the growth of high quality materials. The pure material is widely used in fiber isolators, circulators, beam displacers and other polarizing devices in the optical communication industry. The crystal is a tetragonal uniaxial birefringent material with the space group D [53]. The Yb3+ 4h ions substitute for Y3+ ions in sites of D2d point symmetry. The crystals were produced by Gamdan Optics using the Czochralski growth method at a melting point is 1825 C. Er3+:Y3Al5O12 Current telecommunications infrastructure could be used in a quantum information processing technology based on the 1.5 micron transition of an erbium doped material. Erbium doped yttrium aluminum garnet, Er:YAG, is a well known commercial product in the laser industry. The YAG crystal is cubic and has the same symmetry as the YGG crystal and the Czochralski techniques to grow high quality samples are optimized and multiple different 16 concentrations can be produced. This makes Er:YAG an ideal candidate to perform a full high resolution spectroscopic characterization under various conditions to determine the fundamental physics allowing applications to develop around the material. High resolution absorption measurements of the electronic structure of the excited state crystal field levels of 4I13/2 at the 1.5 micron wavelengths were made. Then fluorescence measurements were made to determine the ground state crystal field levels 4I15/2, time resolved fluorescence and hole decays to measure the excited state lifetimes. The lowest to lowest transition was measured on a 1% and 0.1% doped crystal, showing very little broadening of the 8 GHz inhomogeneous line. However, a 0.05% Er:Y1.5Lu1.5Al5O12 was found to have a 250 GHz inhomogeneous linewidth, which could be quite interesting for wide bandwidth applications. The inhomogeneous line was also measured in the 1% Er:YAG as a function of temperature; a frequency shift was also observed. The linear and quadratic Zeeman effects were mapped as a function of magnetic field strength, up to 7 tesla magnetic field, and orientation using hole burning spectra to determine each of the six erbium sites. The coherence lifetimes were also measured as a function of field, orientation and temperature, and the spectral diffusion. Overall, the coherence lifetime was only weakly dependent on orientation. Rare Earth Doped Powders The powder materials used here are Tm3+: Y3Al5O12 (Tm:YAG), Tb3+:Y3Al5O12: (Tb:YAG), and Er3+:LiNbO3 (Er:LN). The powders were produced and characterized to decide the practicality of using simpler and more economical growth techniques to develop materials for quantum memories and other hole burning applications. 17 Tm3+:Y3Al5O12 Tm:YAG was chosen for study in a powder form because the YAG crystal has been used extensively to host rare earth ions and is used for a wide range of advancements in fundamental material studies and applications [17,36,54,55,]. The material is an excellent host material for the REIs with a cubic unit cell and the inversionless D2 local symmetry of all six Y3+ sites. The yttrium dodecahedral site is a good fit for REI’s size and charge [56]. While the higher symmetry can forbid transitions, the 793 nm transition of interest in Tm:YAG is allowed. Tm:YAG is one of the most promising materials for new quantum or classical information technology systems. With kHz homogeneous spectral lines under a 20 GHz wide inhomogeneous absorption line, information can be stored at 100 Gbits/in2 or higher [61,62]. Tm:YAG is used to process high time-bandwidth signals using coherent light interactions under a multiple patents and can be used as a laser frequency stability reference using spectral holes [63,64]. The branching ratios for a lambda system have also been mapped out enabling spectral tailoring with coherent interactions [57-60]. The lowest energy transition of the 3H6 ↔ 3H4 crystal field levels of Tm3+ in YAG is centered at 793.379 nm. This level can be programmed and characterized with commercially available lasers, such as the Titanium:Sapphire laser, GaAlAs semiconductor diode lasers, as well as frequency doubled 1590 nm lasers. Thulium has the advantage of having an even number of electrons and only a single isotope, 169Tm, which has a ½ nuclear spin. The even number of electrons implies non- degenerate electronic states. Each electronic state only has Zeeman splittings in a magnetic field due to the ½ nuclear spin of thulium giving two levels in the excited state and two in the ground state [54]. Energy levels can also be split due to superhyperfine interactions with the nuclear 18 spins of the host material. The 27Al super-hyperfine energy level structure can also be resolved using spectral hole burning. The lifetimes of the thulium nuclear spins in Tm:YAG are shown to be strongly affected by the fabrication process. The quality of the material was characterized over a large dynamic range by measuring the hyperfine spectral hole lifetimes. Persistent population storage in the nuclear spin hyperfine state of Tm:YAG has long lifetimes, optically pumped and probed using a tunable laser on the order of hours. The resolution of the super- hyperfine levels is used as a measure of the powder material quality along with SEM and XRD. High energy and low energy types of crushing and ball milling were used to produce the Tm:YAG powder material. Several different annealing processes were used to relieve the strain in the material after it was crushed. After annealing powders of Tm:YAG in a tube furnace, the coherence properties of the bulk crystal could be largely re-established in powders that were ground by hand. However, the amount of strain induced into a powder during the grinding is not always completely removed by the annealing process. Annealing at temperature up to 1400 C did not provide enough thermal energy to drive the mechanically induced defects back into a configuration that could regain the REI’s coherence quality in the bulk crystal. Tm:YAG powder was also produced using the co-precipitation aqueous solution fabrication technique [65]. A flux material such as Li2CO3 can be used to lower the melting point of the YAG powders. The flux changed the surface and shape of powders producing dodecahedral crystallites and increased the growth rate at lower temperatures. However, contamination can then become an issue and can increase the decoherence of the material. The growth of the powders does not induce strain in the material like the mechanical crushing, so if 19 the impurities could be removed the powder growth could be an ideal way to survey Tm:YAG and various iterations of the crystal and many different REI doped materials Er3+:LiNbO3 Er:LiNbO3 erbium lithium niobate (Er:LN) is a desirable material for high bandwidth quantum and classical information processing with narrow homogeneous lines under a wider inhomogeneous line, with an unusually strong transition in the telecommunication C-band. The host material is also well known to many industries and can be fabricated into devices. Furthermore, the push to smaller size, weight, and power in all technology has increased the demand for nanofabrication of optical devices. However, few studies have been done on how reducing the size of the crystal material will affect the optical and coherent properties. LN is the most produced transparent single crystal globally, with a production of over 50 tons per year. The growth of the LN crystal was developed at Bell labs [66]. It has been used for linear and nonlinear devices, in situ biological imaging, modulators, lasers, and waveguides [67]. The congruent melting point is significantly non-stoichiometric (48.6 mol% of Li2O). Thus, most of the material is produced congruently, however stoichiometric LiNbO3 can be grown [68] and is of great interest [69]. LN has many properties that make it particularly interesting, including the ability to dope the crystal with a wide variety of ions and all the REIs. The telecom wavelength transition of Er:LN makes it a particularly useful and interesting material for applications. Good coherence properties under a wide inhomogeneous absorption along with an unusually high oscillator strength in the transition of interest allow lower concentrations of erbium if needed, which also has the advantage of limiting the decoherence from Er3+-Er3+ interactions. 20 The crystal displays 3m point symmetry with a trigonal lattice structure described by the R3c (no. 161) space group. The shifting of the lithium and niobium ions makes the material ferroelectric, with a curie temperature of 1210 C. By symmetry, lithium niobate is piezoelectric, pyroelectric and birefringent [66]. This richness of exploitable physical properties and availability has enabled widely-varied research to be performed on the crystal. There are even references to a “Lithium Niobate Valley” in the future where the crystal will surpass the use of silicon [70]. In this study, the coherence properties of Er:LN were characterized using three complementary techniques; spectral hole burning, two-pulse photon echoes, and free induction decay. The three techniques were needed due to the large dynamic range of coherence properties seen between fabrication runs. Tb3+:Y3Al5O12 The Tb3+ doped yttrium aluminum garnet was of interest because the energy level structure would prove that REI materials can be engineered to minimize the phonons that exist in the material. The phonons can be restricted by designing the material to be smaller than the phonon’s wavelength [38]. Most of the phonon density of states can be quenched by lowering the temperature of the material to liquid helium temperature. However, the lowest energy phonons can still be present at 3 kelvin. This is because the lowest energy phonon modes are proportional to the acoustic velocity of the material. YAG has a relatively high acoustic velocity of 6400 m/s. Thus, the shortest wavelength phonon mode can in the powders are smaller than ~100 nm. Therefore, particles under 100 nm should not support phonon vibrational modes. 21 The lowest crystal field energy levels of Tb3+:YAG in the 5D4 excited state have a splitting of only 35 GHz. The small energy gap can be bridged by low energy phonons present in the material. By observing the population difference between the two crystal field energy levels the density of states of the lowest phonon energy mode could be monitored. A Cone Lab built nitrogen laser pumped a Hänsch-type blue dye laser to excite the 5D4 levels of Tb3+. A double monochromator was used to resolve the 35 GHz difference between the fluorescence peaks from the two lowest 5D4 crystal field levels in the excited state of the Tb:YAG powders. The population difference between the two states was monitored by comparing the relative area of the two fluorescence peaks. Minimizing the density of phonons in the material by making the powders smaller could be determined when the higher energy fluorescence peak was smaller in magnitude due to less population in the energy level. The optical relaxation dynamics were correlated with other factors, including the crystal powder fabrication techniques, the crystalline structure and powder properties such as size, morphology and phase. An in-situ temperature measurement of the material was also made by monitoring the relative population of the two lowest levels in the ground state, which is separated by 85 GHz, equivalent to a temperature of about 4 kelvin. Synthesis of Rare Earth Doped Crystals An overview of single crystal growth is given to focus on essential parameters of the Czochralski (CZ) method normally used in growing single crystal oxide materials used here. Several different powder growth techniques were used to produce small crystallites of REI materials compared to each iteration and characterized relative to a single crystal to decide which production technique is most suitable to produce high optical quality REI materials. 22 Single Crystal Growth Many different methods are used to produce large single crystals, ranging from high temperature melts to room temperature aqueous solutions. However, the single crystal oxides used in this work can only be grown using a high temperature or high pressure system. The Verneuil process is regarded as the first synthesis of high temperature single crystal gems, and the first rubies were grown using it. Verneuil presented his sealed notes at the Paris Academy of Science in 1891 but only announced his discovery ten years later in 1902. The method is still used today for crystal growth, and many other techniques have been developed since, including the Czochralski, Bridgeman, floating zone, and Kyropoulos methods. For us, the most notable technique was developed by Jan Czochralski. While studying the crystallization of metals in 1917, he accidentally dipped his pen into a crucible of cooling molten tin and pulled the first crystal out of a melt of the molten material. He could not have imagined the technological and industrial usefulness of this crystal growing technique for our society. The After WWII, the technique was optimized at Bell Labs to grow large single crystals of germanium containing p-n junctions [44]. Czochralski Method The Czochralski or CZ method is now the preferred method for growing high- performance single crystals we rely on today, including silicon, gallium arsenide, sapphires, and REI doped oxides, silicates, vanadates, niobates, fluorides and many others. Moreover, the general design developed by Czochralski over 100 years ago is still being used today to produce new optical technologies because large crystal boules grown and fabricated for devices. 23 The CZ method uses a seed crystal dipped into a melted mixture of the material to be grown. Then, the crucible is held slightly above the melting point of the material of interest; the grown material is delicately pulled while atoms or molecules transfer from the liquid melt to the solid crystal surface in atomic order. Parameters of CZ Growth Technique A Czochralski growth apparatus can be divided into two systems, the furnace and the pulling system. The design of the furnace has a significant effect on the thermal axial and radial gradients and the stability of the temperature. The pulling system influences the melt flow dynamics by controlling the rotation rates of the seed and the diameter of the crystal. Each type of crystal will also require different care on cool down procedures to prevent strain and cracks. The coverage of all parameters of the CZ process is beyond the scope of this work. However, some specific points have a considerable influence on the quality of the materials grown. The interface between the solid and liquid is of particular interest for the growth of all crystals because that is where the atoms are solidified into place, and the crystal structure is formed. The solid-liquid interface in the CZ method can be concave, flat, or convex into the melt. A fluctuating interface has been shown to produce problems in many types of crystals [42], including thermal stresses, facetted interfaces, crystal cracking, impurity inhomogeneities, core segregations and changes in stoichiometry. Therefore, the interface needs to be controlled throughout the pulling of the CZ crystal growth. There are three distinct stages of the growth, the shouldering, the body, and end growth, where the rotation and pull must be monitored to ensure the interface is stable to produce high quality materials. 24 The parameters that give the greatest control of the interface are the rotation rate, pulling rate, and thermal gradients. The rotation and pulling rate can control the flow direction of the melt, the dynamics of the melt gradients and the shape of the interface. The thermal gradients depend on the diameter of the crucible and crystal and the shape and depth of the interface, which can lens blackbody radiation into the crystal having significant effects depending on the absorption profile of the material. Radiative heat loss from the top of the crucible is the main mechanism for the loss of thermal energy from a CZ system and the main cause of thermal gradients outside of the crystal and melt. After-heaters can be used to control thermal gradients as necessary to prevent the crystal from cracking and breaking when cooling to room temperature. Powder Synthesis of REI Doped Materials Powder materials can be synthesized by two general methods, from the “bottom-up” or “top-down.” Chemical synthesis or producing powders from the bottom up, starts with separate chemical constituents that are reacted to produce the composition and phase of the powder desired, and ideally, the size and shape as well. Two different chemical methods were used to produce powders: the solgel technique and the co-precipitation technique. The advantages of these methods include low sintering temperatures, good morphology homogeneity, and distribution of particle sizes that can be made. The final stage of both methods is a solid-state reaction, where the starting reagents have small volumes and large surface areas to maximize the contact between reactants. The top-down route uses mechanical grinding or fracturing processes on a single crystal of the necessary material composition to produce a powder of the desired size and morphology. 25 Pechini/SolGel Chemical Synthesis of Powders The Pechini or SolGel method is a chemical synthesis route for oxides that can be performed in a solution surrounded by a gel that allows oxides to be produced at temperatures below their melting point. For example, using an aqueous solution of metal (M) alkoxide, M- OC2H5, where the hydrolyzed precursor forms to make a polycondensation gel of M-O-M that are cross-linked and uniform. The gel is aged for 24 hours and dried at 300 C to remove water and residual organics. Higher temperatures are then used to synthesize the powder into the crystal phase of interest using temperatures lower than the melting point of the specific material’s phase. Co-Precipitation The co-precipitation method relies on a source of ions in an aqueous solution to react by adding a precipitating agent, ammonium bicarbonate, or ammonia. The precipitating agent was mixed dropwise into the solution to precipitate a precursor powder of the two constituent metals such as aluminum and yttrium in an aqueous form. Oxides of the starting material can be used as precursors but need to be dissolved in an aqueous solution such as nitric or hydrochloric acid. Tm:YAG was synthesized using the co-precipitation method by dissolving nitrates into an aqueous solution with ammonium bicarbonate. The precipitate was stirred in solution to ensure the full reaction is complete. A polar soluble polymer such as polyvinylpyrrolidone was used in the solution to keep the precipitate from agglomerating. A centrifuge was used to separate the size of particles of interest, which are then filtered and washed to eliminate residual unwanted material. The thermal processing on the precursor powders consists of drying the materials above 26 100 C and finally sintering the material at high temperatures between 1000 C and 1500 C, significantly lower than the 1950 C melting point of the bulk YAG materials. Mechanical Processing of a Single Crystal into Powder The mechanical processing of a single crystal into powder consists of crushing the crystal into smaller pieces using various processes. Larger crystal can be thermally cycled to break into smaller pieces, but more grinding or milling is needed to produce crystals powders with diameters between 500 µm and 10 nm. Smaller pieces can be crushed by hand using a mortar and pestle, a vice or press. Low and high energy ball mills were used to produce powders, and results were compared to determine if the impact energy on the millings balls would produce more strain in the powdered REI doped crystals. Although crushing and milling processes introduce significant strain into the crystal, annealing the powder materials can relieve strain, especially if the parent bulk material was not significantly strained. Powders Post Processing Annealing can repair the crystal powders to be the same quality as the bulk crystal in some cases. Temperatures close to the materials melting point are favorable to relieve strain in oxide materials, where lower temperatures do not supply enough energy for the defects to be significantly moved in the material. A tube furnace is used in annealing runs where the atmosphere is controlled; however, the peak temperature of our tube furnace was limited to 1400 C continuously. A high temperature box furnace was also used in later experiments, annealing materials up to 1600 C continuously. 27 Summary of REI Doped Material Properties Synthesis of many REI doped materials for optical applications uses high temperature techniques. The materials studied here are rare earth doped insulating oxides of YAG, LN, YGG, and YSO in the form of single crystals and powders. The REI include thulium, erbium, and ytterbium with concentrations as low as 2 ppm up to a few atomic %. Several techniques were used to produce REI powders, which we compared to single crystals grown using the CZ growth method. Both powders and single crystals have their advantages. Powders can be produced in multiple different methods to be surveyed quickly and are much less expensive to produce. However, they can have unexpected problems such as excessive strain, impurities, agglomeration, and surface effects. Single crystals have the advantage of being easily handled, cut, and oriented with respect to the crystal symmetry and polished to produce smooth surfaces with less optical scattering. However, single crystals are expensive to produce making it hard to iterate between growth parameters. Overall, fabricating and using both forms of the material and characterizing them with high resolution optical techniques can provide the best solution to finding new and exciting materials for the next generation of technologies. 28 CHAPTER 3 CHARACTERIZATION METHODS AND EQUIPMENT Overview of Characterization REI transitions characterized during this work range from the ultraviolet through the visible into the infrared. The REI’s presented in the following chapters include terbium, thulium, erbium, and ytterbium. These measurements build on the wide variety of equipment, knowledge, and crystal materials studied over decades in the Cone/Thiel Rare Earth Spectroscopy Lab. The REIs presented here were chosen because of their respective transition wavelengths and relevance to the coherence and other optical properties needed for applications. High resolution optical spectroscopy is the main characterization tool used when studying rare earth ions in crystals. Imaging, structural, and chemical characterization techniques are also used to draw correlations between traditional material properties and optical properties. Crystal structural tools such as x-ray diffraction techniques were used to determine the crystalline phase of new materials. Laue x-ray and optical birefringence were used to find the orientation of single crystals before performing spectroscopy. Finally, the powders’ size, morphology, and facets were characterized using optical imaging and scanning electron microscopy. Optical Spectroscopy Equipment Optical Components The optical experimental setups include light sources, optics, cryostats, detectors, electronics, and computers. Each REI transition requires different lasers, window coatings, 29 fibers, and detectors. For the highest resolution spectroscopy stable lasers are needed, and preferably a laser system that scans across a wide optical frequency range without mode hoping or large variations in output power. Often the limiting factor in measuring REIs is the laser’s linewidth or the ability to tune a laser across the frequency of the REI transition. Single-mode diode lasers are becoming more common at a few of the REI wavelengths of common use, such as 795nm Tm3+, the 980nm Yb3+, and the 1535nm Er3+ transitions. Moreover, with commercially available laser diodes, external cavity diode lasers in the Littrow or Litman- Metcalf configuration can be built or purchased for tunable spectroscopic characterization. The measurements on the erbium ion in Chapter 5 and 10 used external cavity diode lasers (ECDL) in the Littman-Metcalf configuration. Erbium doped fiber amplifiers were also used to increase the optical power while preserving single mode narrow laser linewidth of the ECDL. In Chapter 7 the ytterbium transition was probe with a home built ECDL in the Littrow configuration. For thulium experiments, a Coherent 899-21 Titanium-Sapphire tunable bow-tie ring laser is a workhorse in the near infrared because of the tuning range, narrow spectral linewidth, and high output power. The terbium fluorescence measurements used a lab built pulsed nitrogen pumped Hänsch-type dye laser, using 6 ns pulses and Coumarin 481 dye to provide the 485 nm photons. 30 Figure 3.1. Image of a Coherent 699 Dye ring laser being pumped with a 532 nm laser. Wavelength dependent optical components such as polarizers, mirrors, isolators, acoustic optical modulators, fibers, Fabry–Pérot interferometer, wavemeters and even lenses or windows with coatings should be optimized for the REI transition of interest. Lenses are usually borosilicates and can be coated with multiple layers of dielectric material to reduce reflections. Quartz and other single crystals can also be used in specific applications. Silver mirrors have the best reflectivity across the visible range, while aluminum is a cheaper alternative; it has a significant loss in the near IR region where gold is superior. Dielectric coated mirrors are used when the highest reflectivity is needed. Broadband light sources such as tungsten halogen lamp are used for wide spectrum absorption scans, and mercury lamps, LEDs, or the appropriate lasers are used for fluorescence excitation. The detectors in this work can be split into visible and 31 infrared. Photomultiplier tubes or silicon diodes are used in the visible and indium gallium arsenide diodes, or germanium detectors are used in the near-IR wavelengths. Cryostats The optical measurements of REI crystals are performed at liquid helium temperatures. Cryostats are common to all optical experiments, and various types of cryostats are used to achieve the needed temperature ranges, magnetic fields, RF inputs, and optical access to the crystal. The two basic helium types of cryostats are open liquid helium bath and closed cycle helium refrigerators. Bath cryostats hold liquid helium in a dewar and bathe the crystal in the liquid or near liquid helium gas. Two open helium bath cryostats were used in this work including an Oxford SpectroMag and an Oxford Optistat. The SpectroMag is equipped with a superconducting split solenoid capable of producing up to eight tesla magnetic fields, and it can be kept cold for several days after being filled. The Optistat can hold temperatures below 2 kelvin for 12-16 hours. A lab-built water-cooled Helmholtz coil is used with the Optistat to produce fields up to 250 Gauss at 45 Gauss/Amp. The most common close cycle cryostats include pulse tubes and Gifford-Mcmahon types. Recently developed technologies were also used in experiments, including helium sorption fridges manufactured by PhotonSpot and a sub-2 kelvin closed cycle pumped liquid helium cryostat manufactured by Montana Instruments, as seen in Figure 3.2 32 Figure 3.2. Five different cryostats used in this work. Top Left: Montana Instrument’s C2 closed cycle Gifford-McMahon system. Top Center: Oxford SpectrumMag helium bath cryostat. Top Right: PhotonSpot’s helium sorption fridge. Bottom: Cryomech’s closed cycle pulse tube in the silver cylinder and Roger Macfarlane aligning a beam through an Oxford Optistat. 33 Materials Characterization of Resonant Frequencies through Optical Spectroscopy When new REI doped materials are produced, absorption and fluorescence spectroscopy are often the first optical measurements performed. Optical absorption spectroscopy is used to measure the absorption of excited state energies along with the inhomogeneous linewidths, center frequency, and absorption coefficients of the transitions. Fluorescence spectra are used to find the energy levels of the ground multiplet, and time resolved fluorescence decays allow the excited-state lifetimes to be quantified. Once the wavelength of the transition of interest is identified, lasers are employed to further characterize the material with higher resolution techniques. The optical coherence properties of REIs are useful for applications, so they are often of the greatest interest to the REI and quantum information community. The coherence lifetimes and spectral hole burning structure can also be used as a sensitive characterization tool to determine material quality. Techniques such as photon echoes, spectral hole burning, and free induction decays can be used to measure coherence lifetimes over a large dynamic range. Nuclear-spin frequencies, lifetimes, and spin coherence can also be used to probe the properties of the REI doped materials, giving insight into the REI quantum structure as well as the host quality. Magnetic fields are often used to study the Zeeman interactions of the REI’s spins. Radio frequency oscillators can also be used to drive the low energy spin transitions to study their dynamics which are of interest for microwave to optical transducers and quantum memories. Absorption and Fluorescence The excited state crystal field energy levels of REIs are characterized and identified using optical absorption measurements. The REI energy levels of interest are cataloged for many 34 common REI doped crystals by Morrison and Leavitt [2]. However, the linewidths, absorption coefficients and relative oscillator strengths of individual crystal field transitions need to be measured, since they depend on specific crystals, crystal composition and history. A broadband lamp and a spectrometer or optical spectrum analyzer are used to detect the amount of light transmitted by the material. Filters should be used to select ranges of light when using broadband sources to reduce the heat load on the crystal and minimize the involvement of REI transitions out of the range of interest. The spectrometers used are the SPEX 14018 and the SPEX 1000; each uses dispersive gratings to filter the light have a resolution of 0.1cm-1 = 3 GHz. When using a spectrometer, the slit widths should be optimized for resolution; the wavelength should be calibrated with an absolute frequency reference, such as a laser, a uranium lamp, or a mercury lamp. Multiple calibrations should be taken if measurements are made throughout the day to ensure the highest accuracy because pressure and temperature fluctuations in the room can also cause changes to the index of refraction of the air. The optical spectrum analyzers (OSA) use a dispersive grating or a Michelson interferometer. The Michelson interferometer OSA uses a He-Ne laser as a reference with a resolution of 900 MHz in the 1550 nm range and drops slightly as the wavelength decreases toward the visible. Accurate measurements require the absorption transition to be detectable, ideally with an optical density no greater than αL ~ 1, because over-absorbed transitions give nonlinear results and materials with low absorption can be difficult to measure. The inhomogeneous width also gives a sensitive measurement of the distribution of the rare-earth ion’s local environment and the degree of order in the crystal [34]. The crystal can be cut thin to make accurate measurements if a transition is over absorbed. In some cases, very thin samples are needed where high oscillator 35 strengths and narrow inhomogeneous linewidths can give REIs very high absorption coefficients. For example, a Yb:YVO4 crystal with only 10 ppm of Yb needed to be cut down to 90 µm. Materials with broader inhomogeneous lines and lower absorption coefficients require longer samples and higher concentrations to achieve an optimal optical density, as in the case of Tm:YGG, in Figure 3.3, which needs to be ~10 mm and a concentration of 2% to have an αL ~1 Figure 3.3. Absorption spectra of the 3H4 levels of 3%Tm:YGG. Laser absorption spectra can show high-resolution detail when the linewidth is too narrow to resolve with the spectrometers. Tunable lasers also can selectively excite specific absorption lines of rare-earth ions to identify transitions with a specific site, a capability especially useful for crystals with multiple sites or defect sites. Narrow lasers that scan rapidly, often by current or piezo tuning, are needed for precise measurements. Low laser power should 36 always be used to prevent optical broadening and spectral hole burning, altering the absorption coefficient and linewidths [71-73]. Fluorescence spectroscopy is used to observe the photons emitted by the material after the ions have been excited by a resonant light source to an excited energy level. The energy levels of the ground-multiplet are measured using the spectrometer to scan across the energies of the fluorescence peaks. For example, the energy level structure of 4I15/2 was determined by exciting the sample with a broadband tungsten-halogen lamp and recording the fluorescence spectra using a SPEX1000M spectrometer with 3 GHz resolution and a liquid-nitrogen cooled germanium photodiode. The highest energy fluorescence peak will be at the same energy as the lowest energy absorption peak when symmetry allows the lowest-to-lowest transition to be observable. The sources used are lasers and high-powered broadband lamps such as mercury vapor or a xenon lamp. Once the wavelengths of the transitions of interest are identified, a resonant laser can be tuned for direct excitation. Time-resolved fluorescence is used with pulsed excitation sources to determine excited-state fluorescence lifetimes, relaxation mechanisms and decay pathways. Spectral Hole Burning Spectral hole burning (SHB) is an optical pumping process that occurs when a laser excites an ensemble of ions of an inhomogeneous absorption line into an excited state. The ions are optically burned out of the absorption profile, leaving a spectral hole. Spectral holes can only be burned into materials with inhomogeneously broadened absorption lines, usually requiring low temperatures. REI doped solids cooled to low temperatures reduce the homogeneous broadening by phonons, produceing inhomogeneously broadened absorption lines. 37 The detected spectral hole is at least twice the intrinsic homogeneous linewidth of the transition because the laser is on the transition twice; it is burned and scanned to measure the width. Laser jitter, power broadening, and spectral diffusion also increase the linewidth. The population lifetime and decay pathways can be determined by measuring the decay of the spectral hole through time-resolved hole burning. If the hole lifetime is limited by the excited-state or an intermediate bottleneck state, it is known as a transient spectral hole. Longer lived persistent spectral hole population reservoirs can be Zeeman levels, hyperfine, or superhyperfine levels. Optical pumping of hyperfine and superhyperfine states in materials can produce persistent spectral holes lasting minutes, hours, and even week. In Tm:YAG and Er:LN, the nuclear spin state lifetimes are used to assess the quality different fabrication methods of the materials. Photon Echoes Two-pulse photon echoes use a sequence of optical pulses that effectively remove the inhomogeneous broadening to measure the coherence time, T2, the homogeneous linewidth, Γh, where T2=1/(πΓh). The ultimate limit for T2 is set by the excited-state lifetime through the relation T1 ≤ 2T2. A truly isolated ion would exhibit a natural linewidth caused by the finite lifetime of the transition; however, this is rarely the case because of heating, ion-ion coupling, and other material dynamics. In rare cases, the homogeneous linewidths can be nearly lifetime limited [13]. Since the homogeneous linewidths may be much narrower than the laser linewidth, the photon echo technique is a convenient way to measure the homogeneous linewidth because it overcomes the laser’s instability. 38 Figure 3.4. Block diagram of a two pulse photon echo experiment where the echo area is measured as a function of the t12 pulse delay. As the pulse delay is increased, the area of the echo is measured. In a two-pulse echo measurement, Figure 3.4 two pulses, the first with a pulse area of pi/2 and the second is nominally double the pulse area and separated in time by τ are used to probe the ions. In practice the second pulse is often slightly smaller than the twice the first pulse area. The first pulse excites an ensemble of resonant ions into a coherent superposition between the ground and excited state. After the pulse, the ions oscillate in phase while the dipole moment produces coherent emission for a short amount of time after the pulse is turned off, emitting a free induction decay. The ions will dephase from each other while they are in the superposition. The second pulse, at a time τ, flips the phases by inverting the transition moment precession, which effectively reverses the dephasing. After the same amount of time, τ, between the pulses the dipoles rephase to produce a coherent pulse of light, the photon echo. For example in Tm:YGG, two-pulse photon echo decays were measured using a laser with a center wavelength at 795.334 nm. A slow continuous scan of 2 GHz per 25 seconds was used to prevent pumping population into the bottleneck state. The optical pulse lengths were set using a pulse generator to open and close an RF switch connected to the synthesizer amplifier, variable attenuator, and acoustic optic modulators (AOMs). The pulse lengths were set as short as possible, down to 100 ns. Two AOMs are used in series to ensure >60 dB attenuation of the 39 continuous laser. A collimated or slightly divergent beam was focused to about 300 µm in the crystal using a 150 mm achromatic lens. The signal was collected from the crystal with the same type of lens for f-matching and then focused through an AOM. The AOM is used as an optical switch to block the pulses and open during the echo signal, dependent on the time delay between the two pulses. Detection was made by a Newport 1801 silicon detector or Hamamatsu R928 photomultiplier tube. The homogeneous linewidths can be measured by recording the exponential decay of echo area as the t12 pulse delay is increased. Below in Figure 3.5 is an example of measured echo decay curves in four different crystals. 1 1% Tm:YGG 4-223 1% Tm:YGG 6-412 2% Tm:YGG 9-0342 3% Tm:YGG 9-0330 0.1 0.01 T = 420 us m 1E-3 T = 136 us m T = 45 us m 1E-4 0 50 100 150 200 250 300 350 400 t Delay (s) 12 Figure 3.5 Two Pulse Photon Echo decays of four different Tm:YGG growths all taken in an Oxford liquid helium bath cryostat at 1.2K. Electron Spin Coherence An experimental set up to characterize the electron spins of Er:YSO was built to explore the properties of the spin lifetimes, and spin coherence. The experiment included an optical and RF system to interact with the resonant splitting of erbium in an external magnetic field. Photon Echo Area (arb.) 40 A static magnetic B field created by an external Helmholtz coil was applied parallel to the D1 axis of the crystal. The sample was mounted onto a lab built SMA coaxial 50 Ω impedance-matched copper strip waveguide through which the RF power passed, producing an RF excitation with an amplitude of several Gauss along the b axis of the crystal. An SMA male- male connector was milled out exposing the bare wire to act as a waveguide along the dimension of the crystal axis to enable the microwave field to interact with the erbium spins resonance tuned by the magnetic field. The RF transmission line was terminated by a 50 Ω impedance load outside of the cryostat to prevent back-reflection. The optical detection after the sample was made by an amplified AC-coupled photodiode (New Focus model 1611-AC) with 1 GHz bandwidth. The acquired signal was sent to a spectrum analyzer to measure the Raman beat amplitude. An HP model E4411B spectrum analyzer with an integrated RF tracking generator to produce an RF signal of -10 dBm between 9 kHz and 1 GHz used for the continuous Raman heterodyne signal. The experiments were set up around an Er:YSO crystal in a helium flow Oxford Optistat cryostat. The laser and the RF field could be pulsed to perform excited state spin coherence measurements on Er:YSO to measure the effect of spin flip flops on the coherence and determined the quantum efficiency of the spin transition, which was found to be near 100%. Powder Characterization Techniques Material properties such as the structural composition, phase, size, and shape, are essential aspects to characterize when studying the fabrication effects on powders. The main non-resonant characterization techniques used are x-ray diffraction and scanning electron microscopy. 41 XRD The compositional phase of each powder was determined using the x-ray diffraction (XRD) instrument at MSU’s Imaging and Chemical Analysis Lab (ICAL). The XRD is a Scintag Inc X-1, Advanced Diffraction System. The x-ray source is run at 1.8 kW, 45kV and 40 mA, using the copper K-α line corresponding to 8.04 keV, which has an x-ray wavelength of 1.5406 Å. The slits on the source used are a divergence slit of 2 mm and a scattering slit of 4 mm. The detector slits used were 0.5 mm scattering and 0.2 mm receiving. Step sizes were set to 0.02 degrees and dwell times of 0.5 seconds at each step. Figure 3.6 shows a typical XRD spectrum with reference peaks. −Tm:YAG Powder −YAG Reference Figure 3.6. XRD spectra of Tm:YAG powder taken in ICAL. The red lines are positions of the prominent peaks of a YAG reference material. Scanning Electron Microscope Powders were imaged using the Zeiss SUPRA 55VP field emission scanning electron microscope at ICAL to determine their size, morphology, and distribution. In Figure 3.7, the left image illustrates the consistency of the powders, with the inset showing a typical amount of material produced from a single production run. The center image shows the well-defined 42 dodecahedral shapes of individual particles compared to the shape of the powders after using high-temperature treatment with metal-halide flux. Figure 3.7. Electron microscopy images of Tm:YAG powders. Left: Images showing a larger field of view of the powders, the inset showing a typical amount of material produced from a single production run. Center: A closer view of the well-defined dodecahedral YAG crystal powders. Right: powders partially melted after being heat treated in metal-halide flux. Single Crystal Orientation Before optical measurements are made the orientation of the crystal should be known. Single crystals oriented with respect to the electric field polarization of the light; the external magnetic field enables fundamental physical tensors to be determined and the optical properties of the materials to be optimized in applications. Birefringence In the case where the crystal is anisotropic, the crystal will be optically birefringent. The birefringence can be used to orient the crystal by simply using crossed polarizers. More details on this are given in Chapter 4, specifically for the case of YSO, with an extension to other crystal symmetries as well. Since LiNbO3 is a uniaxial birefringent crystal, the c-axis can be found by looking at the crystal between crossed polarizers as shown in Figure 3.8. 43 Figure 3.8. Birefringence photographs of LiNbO3. Left: Looking along the optical axis, the c- axis of LiNbO3. Right: Looking along a vertical extinction axis, the optical axis can be seen at the top of the image, showing how a crystal that is not cut along the optical axis looks between crossed polarizers. Laue x-ray Laue x-ray photographs are used to orient single crystals of any symmetry. The Laue system used in this work is housed at Scientific Material’s/FLIR. It is a back scatter Photonic Science Laue camera, with a central hole to allow the x-rays to pass through and diffract off the face of the crystal back onto the CCD camera. The crystal is adjusted on a goniometer to find the symmetrical orientation. The program Orient Express is used to align a simulated image with the real image taken. Figure 3.9 shows a backscatter image of a YSO crystal overlayed with a simulated image on the left. On the right, the image is overlayed with the crystal axes and the dielectric axes. 44 Figure 3.9. The backscatter reflection points of YSO observed with Laue X-rays. Left: The image is overlaid with the simulated points using Orient Express software to determine the orientation of the crystal. Right: The backscatter photo showing the orientation of the crystal axes with respect to the reciprocal lattice points and the dielectric axes. Acid Etching Chemical etching is used to find dislocation density and inclusion defects such as iridium particles arising from CZ growth or processing. In combination with optical birefringence patterns the Burgers vectors of the dislocations can be revealed. Phosphoric acid is the most common chemical etching solution for the rare-earth garnet crystal system [74]. The temperature range of 250-450°C is the preferred approach for etching the surface and “chemically polishing” the crystal to remove the higher density of shallow surface defects that are normally caused by crystal cutting and mechanical polishing. The optimal temperature for the common crystals YAG and GGG is ~435C and ~300C, respectively, suggesting a temperature near 300C should be employed for YGG, with a longer pre-etch at a lower temperature of 160C to clean the surface and enhance the uniformity of the later strong etch. Etching the {110} surface plane of the crystal shows the characteristic facets of the cubic symmetry, which can also be used as orientation markers seen in the right image in Figure 3.10. 45 Figure 3.10. Microscope image of etched surface of a {110} plane perpendicular to the <211> axis of a Tm:YGG sample. The etch was done with phosphoric acid for 1 hour at 200 C. We have applied the acid etching approach to characterize the type and density of defects of as-grown and post-anneal crystals to quantify the effects of annealing on the large-scale lattice defects. Etch pits can also be used to help verify the orientation of single crystals. Chemical Composition Mass spectrometry is used to measure impurities across the periodic table that may be difficult to detect using other techniques. Several different mass spectroscopy techniques were used to measure impurities in the crystals; these include inductively coupled plasma mass spectroscopy (ICP-MS), glow discharge, and laser ablation-ICP-MS. The time-of-flight secondary ion mass spectroscopy in ICAL was used to measure the chemical compositions as a function of depth for lithium niobate wafers with rare-earth ions diffused into the surface. Using a pulsed positive gallium ion gun to sputter material from the surface, the secondary ions are accelerated by ion optics through a series of magnetic fields and 46 the masses of the ions are separated by the time of flight. Depth profiles are achieved by using the ion gun to sputter an area of known spatial resolution >10 µm2, then collecting the emitted secondary ions. The depths sputtered are measured with an atomic force microscope and sputtering rates can be determined for different crystals and orientations. Two different methods were used to compare the concentrations of impurities in YSO. Two crystals were sent to EAG Labs to be analyzed by glow discharge and they were also analyzed by laser ablation coupled with an ICP-MS. The concentrations of impurities in the Tm:YGG crystals show a significant amount of aluminum and silicon in all of the crystals . The original 1% Tm:YGG #04-223, which has the longest coherence, shows a larger amount of transition metals. Other impurities such as calcium and zinc are seen in the newer growths. There can be discrepancies in the absolute amount parts per million of impurities in each crystal due to contamination of the system from previous samples measured. However, the relative amounts in each crystal can be used as an indicator of the influence of the different ions on the optical coherence properties. It should also be noted that Y2SiO5 was analyzed in the system before the YGG and argon (AMU=40) is used as a carrier gas. In Figure 3.11, the full scan of impurities is given to show a wide spectrum of elements. Two scans were performed on the 1% Tm:YGG #04-223; the first was taken with a smaller number of elements to test the results. The concentrations that are significantly higher than expected are highlighted. 47 Figure 3.11. Concentration of impurities in three different Tm:YGG crystal growths using the Iridia Teledyne Photon Machines Laser Ablation Inductively Coupled Plasma Mass Spectroscopy The Al and Si are much higher than expected, but this could be from background contamination. A few elements may have an interference peak due to ion combinations. For example, the Pd concentration is likely a yttrium ion and an oxygen ion recombining before striking the detector. The masses of yttrium and gallium are near the Gd and Tb, measured to be in excess in all the scan except the 2% Tm:YGG #03-0986, which needs to be researched further. Other concerning impurities are the Pb, which is slightly higher than expected, and Zr, which is used as an insulating material in the furnaces used in the growth of the material. The Cd is most likely an artifact of other charge/mass ratios. The Fe, V, and Ce are all higher in the original crystal #04-223, which has the longest coherence suggesting the ions either help lower decoherence or have a minimal effect. The impurities of most concern in the newer crystal, #09- 0330 and #03-0986, are the Ca, Zn, and to a lesser extent, the Lu. 48 1% Tm:YGG 1% Tm:YGG 3% TmYGG 2% TmYGG #4-223 #04-223 #09-0330 #03-0986 Tm:Y3Ga5O12 05-Nov-20 12-Nov-20 Element Atomic Mass Concetration [ppm] Al 26.98 737.60 455.30 123.00 Si 28.09 2354.00 608.30 704.40 P 30.97 11.48 9.09 27.65 Ca 40.08 1.11 41.95 24.17 Sc 44.96 0.37 axis which is also a dielectric axis labeled as the b-axis. The a and c crystal axes lie at an obtuse 102 degree angle to each other and orthogonal to the b-axis [47,48,83-85]. The three principal dielectric axes are always orthogonal to each other and make-up the index ellipsoid or optical indicatrix. Designated here as b, D1, and D2 corresponding to X, Y, and Z axes labeled by Beach et al. The D2 axis has the highest index of refraction, the b axis has the lowest index and the D1 axis is the intermediate principal index. YSO a positive biaxial crystal because the intermediate index, D1, is closer in magnitude to the largest index axis, the D2 axis. Therefore, the optical axes are closest to the D2 axis in the optical plane. The 2V angle, the acute angle between the optical axes, is ~40 degrees and the D2 axis bisects this acute angle, making it the acute bisectrix. The b axis is the obtuse bisectrix, and the D1 is the optical normal. The geometrical arrangement of these features is shown in Figure 4.1. 54 Figure 4.1. The optical plane and axes of YSO, showing a positive biaxial crystal with a 2V angle of ~40 degrees. Laue X-Rays backscatter images were also taken to confirm the relationship between the crystal axes and the D1 and D2 axes. The a crystal axes of YSO is ~23 degrees from D1, dielectric axis and the crystallographic c-axis is ~11 degrees to the D2 dielectric axis at a wavelength of 650 nm [86]. The direction of the b-axis is ambiguous in other references so here we use a right-handed coordinate system and define the positive direction of the b axis is out of the page in Figure 4.2. 55 Figure 4.2. The crystal axes (solid colored lines), and the dielectric axes (black lines, horizontal and vertical) overlaid with the Laue x-ray points of YSO. The reciprocal lattice vectors (dotted colored lines) observed using Laue x-rays reflection photographs show D1 is about 23 degrees from the crystallographic a-axis, and D2 is about 11 degrees from the c-axis at a wavelength of 650 nm. The positive direction of the b axis is defined to be pointing out of the page. Location and Identification of the Extinction Axes Crossed polarizers or a polariscope can be used to find the principal axes of the optical indicatrix via extinction [86-88]. The polariscope consists of a pair of crossed polarizers and a diffuse light source, seen in Figure 4.3. When the crystal’s dielectric axes are aligned with one of the polarizer’s axes, the transmitted light will be nulled indicating an extinction axis. Each of the three extinction axes can be easily seen using a polariscope and a crystal that has been polished sufficiently to not scatter the polarized light. An index matching fluid such as acetone can also be used on unpolished crystal surfaces. 56 Figure 4.3. (Left) Commercial gemological polariscope. Example of YSO’s extinction axes observed using a polariscope, Fig (Center) viewing the crystal along the D1 or D2 axis. (Right) viewing the crystal along the b-axis shows the change in transmission because of the rotation of the dielectric axes. The optical indicatrix rotates about 2 degrees in the visible wavelength range [90,91] about the b-axis as the wavelength is varied. The rotation is enough to see the change in the transmitted color of light. This can be used as a convenient way to distinguish the b-axis from the D1 and D2 axes of crystal. When the polariscope and crystal transmits blue light, the extinction axes corresponding to red wavelengths are aligned with the polarizers, as seen in Figure 4.3. The rotation of the dielectric frame is not seen when looking along D1 or D2, axis in the polariscope, because the b-axis does not change with wavelength since it is fixed to a crystallographic axis. It should be noted that if the D1 or D2 -axis is not exactly normal to the polarizers, components of the index ellipsoid can cause slight color changes. Direction of the b-axis The positive and negative direction of the b-axis must be found for the complete orientation of YSO. There is not a standard defined for the direction of the 2/m symmetry, thus 57 the convention of Beach et al and a right-hand coordinate system of the crystal axes is used to define the direction of the b axis. Thus, in Figure 4.2 the b axis is out of the page. To find the direction of the b axis optically the rotation of the index ellipsoid about b axis with wavelength can be used. If the transmitted colors of a YSO crystal in a polariscope appear from red to blue when the crystal is turned in a clockwise rotation the positive b axis points towards the viewer. Conversely, when the color of the light transmitted through the extinction axes and crystal changes from blue to red in a clockwise rotation, the positive b axis is pointing away from the observer, as depicted in Figure 4.4. Figure 4.4. Diagrams showing the extremes of the transmitted color seen visually with the rotation of the crystal between crossed polarizers. The dielectric axes change as a function of wavelength relative to the crystal axes indicating the direction of the b axis. Using a Conoscope to Locate and Identify the Axes A conoscope is a high numerical aperture lens used with the polariscope, which can be used to locate and identify the dielectric axes. The conoscope converges the white light in the polariscope allowing the observer to see a range of optical paths through the crystal in one view. 58 Figure 4.5 A photograph of YSO’s birefringent pattern looking along the D2-axis using crossed polarizers and a conoscope. The horizontal b-axis and vertical D1-axis are aligned with the crossed polarizer axes. The blue and red fringes, parallel to and straddling the b-axis, show the rotation of the optical axis and plane. Note the sample shown has the crystal facets cut approximately 5 degrees off from the b and D1 axes. The extinction axes viewed with convergent light are known as isogyres. The isogyres are easiest to see when viewed along the D2 axis, the acute bisectrix due to the proximity to the optical axes. When the crystal is rotated and viewed along the D2 axis, curved extinction axes are seen until the b and D1 axes are aligned with the crossed polarizer axes. The crossed isogyres indicate the alignment of all three dielectric axes relative to the sample faces, as in Figure 4.5. The red and blue light along the b-axis is known as horizontal dispersion and can be used to determine the direction of the b-axis. From this perspective, when blue is observed above the extinction axis and red light is lower on the axis, the positive b-axis points to the left. With a conoscope or polarizing microscope, all three extinction axes can be aligned and defined when the YSO sample is viewed along D2 axis between crossed polarizers. Deviations in alignment of the crystal facets to the dielectric axes can also be determined easily using a conoscope. The 59 direction of the b-axis is also unambiguously determined using the horizontal dispersion as a guide. Biaxial Crystals: Monoclinic, Triclinic, and Orthorhombic Systems The techniques shown in the case of YSO can immediately be applied to other monoclinic crystals, though some points need to be considered. If the symmetry axis is the acute bisectrix or the optical normal, the dispersion will respectively be crossed or inclined around the axis. The crystal’s symmetry axes are easier to visually see if the rotation of the dielectric frame is strong. If the angle of rotation is small a polarizing microscope can be helpful, or a Malus measurement can be setup. The principles of aligning monoclinic crystals can also be applied to other optically biaxial crystals. Each extinction axis is found by nulling the transmitted light in a polariscope or crossing isogyres. If the crystal is positive or negative biaxial, then the extinction axes may then be assigned to the crystal axes based on the relative magnitudes of their respective refractive indices by way of the acute and obtuse bisectrices. In the triclinic crystal systems, each crystal axis will have a direction, as no crystal axis is orthogonal to the others. As a result, the optical indicatrix may freely scale in size, yaw, pitch, and roll as the frequency of light is varied. If the rotation of the dielectric frame of each axis can be observed a sense can be assigned to each axis by relating the rotation of color to the crystal’s corresponding Laue pattern. Using the one direction of dielectric axis all the dielectric axes can be related to the crystal axes. The color pattern may be difficult to view or interpret in some cases as the rotation of the optical plane is unconstrained. 60 Orthorhombic systems have orthogonal crystal axes. Therefore, each dielectric axis is always collinear with a crystal axes, simplifying the relationships between the crystal structure and the optical indicatrix. In orthorhombic materials the optical indicatrix is fixed in place and does not pivot about any axis. Uniaxial Crystals: Tetragonal, Trigonal, and Hexagonal Systems The points covered in the case of biaxial materials also have relevance to the higher symmetry tetragonal, trigonal, and hexagonal crystal systems, which are optically uniaxial. Because there is only one unique refractive index the optical indicatrix will have rotational symmetry about the c-axis of uniaxial crystals. Extinction axes are visible when the c-axis is in the plane of the polarization axes of the polariscope. However, when the c-axis is perpendicular the polarizers, the material behaves isotropically. Only the alignment of the c-axis may be fully specified in a uniaxial crystal using a polariscope. The optically symmetric c-axis can have directionality, as in the case of LiNbO3 [92], which can be distinguished using other thermal or electrical techniques [93] . Isotropic Crystals: Cubic Systems Cubic crystals have orthogonal and equal dielectric axes, therefore optically isotropic and do not possess extinction axes. However, some cubic systems and certain other point groups can show optical activity along specific crystal directions, which may be useful in determining directions in cubic crystals. For more information, the reader is referred elsewhere [93-97]. 61 Conclusion A simple optical technique using crossed polarizers is described to visually determine the optical orientation of birefringent crystals using the material’s wavelength-dependent dielectric frame to quickly and accurately located the materials axes. YSO’s crystal axes are related to optical dielectric indicatrix using Laue backscatter images to define the direction of the b-axis with respect to the D1 and D2 axes. With the relative orientation known between the optical indicatrix and the crystal axes, birefringent crystals can be completely oriented using crossed polarizers. 62 CHAPTER 5 ELECTRON SPIN COHERENCE IN OPTICALLY EXCITED STATES OF RARE-EARTH IONS FOR MICROWAVE TO OPTICAL QUANTUM TRANSDUCERS Contribution of Authors and Co-Authors Manuscript in Chapter 5 Author: Sacha Welinski Contributions: Prepared material samples, designed and set up experimental apparatus, performed measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Philip J. T. Woodburn Contributions: Prepared material samples, designed and set up experimental apparatus, performed measurements to acquire data, analyzed and interpreted results, generated figures, edited the manuscript. Co-Author: Nikolai Lauk Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Rufus L. Cone Contributions: Analyzed and interpreted results, edited the manuscript, discussed results and implications. Co-Author: Christoph Simon Contributions: Analyzed and interpreted results, discussed results and implications. Co-Author: Philippe Goldner Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. 63 Co-Author: Charles W. Thiel Contributions: Prepared material samples, designed and set up experimental apparatus, performed measurements to acquire data, analyzed and interpreted results, generated figures, edited the manuscript. 64 Manuscript Information Sacha Welinski, Philip J. T. Woodburn, Nikolai Lauk, Rufus L. Cone, Christoph Simon, Philippe Goldner, and Charles W. Thiel Physical Review Letters Status of Manuscript: ____ Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-reviewed journal ____ Accepted by a peer-reviewed journal __X_ Published in a peer-reviewed journal American Physical Society (2019) Volume 122, Issue 24 https://doi.org/10.1103/PhysRevLett.122.247401 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 CHAPTER 6 MEASUREMENT OF THE THULIUM ION SPIN HAMILTONIAN WITHIN A YTTRIUM GALLIUM GARNET HOST CRYSTAL Contribution of Authors and Co-Authors Manuscript in Chapter 6 Author: Jacob H. Davidson Contributions: Prepared material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Philip J. T. Woodburn: Contributions: Prepared material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Aaron D. Marsh Contributions: Prepared material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Kyle J. Olson Contributions: Analyzed and interpreted results, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript, discussed results and implications. Co-Author: Adam Olivera Contributions: Analyzed and interpreted results, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript, discussed results and implications. 84 Co-Author: Antariksha Das Contributions: Analyzed and interpreted results, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript, discussed results and implications. Co-Author: Mohsen Falamarzi Askarani Contributions: Analyzed and interpreted results, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript, discussed results and implications. Co-Author: Wolfgang Tittel Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Rufus L. Cone Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Charles W. Thiel Contributions: Prepared material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. 85 Manuscript Information Jacob H. Davidson, Philip J. T. Woodburn, Aaron D. Marsh, Kyle J. Olson, Adam Olivera, Antariksha Das, Mohsen Falamarzi Askarani, Wolfgang Tittel, Rufus L. Cone, and Charles W. Thiel Physical Review B Status of Manuscript: __X_Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-reviewed journal ____ Accepted by a peer-reviewed journal ___ Published in a peer-reviewed journal 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 CHAPTER 7 CHARACTERIZATION OF 171YB3+:YVO4 FOR PHOTONIC QUANTUM TECHNOLOGIES Contribution of Authors and Co-Authors Manuscript in Chapter 7 Author: Jonathan M. Kindem Contributions: Designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: John G. Bartholomew Contributions: Designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Philip J. T. Woodburn Contributions: Designed and set up experimental apparatus, performed measurements to acquire data, analyzed and interpreted results, wrote and edited the manuscript. Co-Author: Tian Zhong Contributions: Designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Ioana Craiciu Contributions: Designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Rufus L. Cone Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. 102 Co-Author: Charles W. Thiel Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Andrei Faraon Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. 103 Manuscript Information Jonathan M. Kindem, John G. Bartholomew, Philip J. T. Woodburn, Tian Zhong, Ioana Craiciu, Rufus L. Cone, Charles W. Thiel, and Andrei Faraon Physical Review B Status of Manuscript: ____ Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-reviewed journal ____ Accepted by a peer-reviewed journal __X_ Published in a peer-reviewed journal American Physical Society (2018) Volume 98, Issue 2 https://doi.org/10.1103/PhysRevB.98.024404 104 105 106 107 108 109 110 111 112 113 114 CHAPTER 8 OPTICAL SPECTROSCOPY AND DECOHERENCE STUDIES OF ERBIUM-DOPED Y3AL5O12 AT 1.5 MICRONS Contribution of Authors and Co-Authors Manuscript in Chapter 8 Author: Thomas Lutz Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Charles W. Thiel Contributions: Conceived of the study, prepared material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Lucile Veissier Contributions: Prepared material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Philip J. T. Woodburn: Contributions: Prepared material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Rose L. Ahlefeldt Contributions: Analyzed and interpreted results, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript, discussed results and implications. 115 Co-Author: Paul E. Barclay Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Wolfgang Tittel Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Rufus L. Cone Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. 116 Manuscript Information Thomas Lutz, Charles W. Thiel, Lucile Veissier, Philip J. T. Woodburn, Rose L. Ahlefeldt, Paul E. Barclay, Wolfgang Tittel, and Rufus L. Cone Physical Review B Status of Manuscript: __X_Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-reviewed journal ____ Accepted by a peer-reviewed journal ___ Published in a peer-reviewed journal 117 118 119 120 121 122 123 124 125 126 127 128 129 130 CHAPTER 9 EFFECTS OF FABRICATION METHODS ON SPIN RELAXATION AND CRYSTALLITE QUALITY IN Tm-DOPED Y3Al5O12 POWDERS STUDIED USING SPECTRAL HOLE BURNING Contribution of Authors and Co-Authors Manuscript in Chapter 9 Author: Thomas Lutz Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Lucile Veissier Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Charles W. Thiel Contributions: Conceived of the study, prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, edited the manuscript. Co-Author: Philip J. T. Woodburn: Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, edited the manuscript. Co-Author: Rufus L. Cone Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. 131 Co-Author: Paul E. Barclay Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Wolfgang Tittel Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. 132 Manuscript Information Thomas Lutz, Lucile Veissier, Charles W. Thiel, Philip J. T. Woodburn, Rufus L. Cone, Paul E. Barclay & Wolfgang Tittel Science and Technology of Advanced Materials Status of Manuscript: ____ Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-reviewed journal ____ Accepted by a peer-reviewed journal __X_ Published in a peer-reviewed journal National Institute for Materials Science in partnership with Taylor & Francis In Volume. 17, Issue. 1, Pages 63–70 (2016) http://dx.doi.org/10.1080/14686996.2016.1148528 133 134 135 136 137 138 139 140 141 CHAPTER 10 EFFECTS OF MECHANICAL PROCESSING AND ANNEALING ON OPTICAL COHERENCE PROPERTIES OF Er3+:LiNbO3 POWDERS Contribution of Authors and Co-Authors Manuscript in Chapter 10 Author: Thomas Lutz Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Lucile Veissier Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript Co-Author: Charles W. Thiel Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, edited the manuscript. Co-Author: Philip J. T. Woodburn: Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, edited the manuscript. Co-Author: Rufus L. Cone Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. 142 Co-Author: Paul E. Barclay Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Wolfgang Tittel Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. 143 Manuscript Information Thomas Lutz, Lucile Veissier, Charles W. Thiel, Philip J.T. Woodburn, Rufus L. Cone, Paul E. Barclay, Wolfgang Tittel Journal of Luminescence Status of Manuscript: ____ Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-reviewed journal ____ Accepted by a peer-reviewed journal __X_ Published in a peer-reviewed journal Published by Elsevier (2017) Volume 191, Part A, Pages 2-12 http://dx.doi.org/10.1016/j.jlumin.2017.03.027 144 145 146 147 148 149 150 151 152 153 154 155 CHAPTER 11 MODIFICATION OF RELAXATION DYNAMICS IN Tb3+:Y3Al5O12 NANOPOWDERS Contribution of Authors and Co-Authors Manuscript in Chapter 11 Author: Thomas Lutz Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Lucile Veissier Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Philip J. T. Woodburn: Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Rufus L. Cone Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Paul E. Barclay Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Wolfgang Tittel Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. 156 Co-Author: Charles W. Thiel Contributions: Prepared and synthesized material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. 157 Manuscript Information Thomas Lutz, Lucile Veissier, Philip J. T. Woodburn, Rufus L. Cone, Paul E. Barclay, Wolfgang Tittel, and Charles W. Thiel Physical Review B Status of Manuscript: ____ Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-reviewed journal ____ Accepted by a peer-reviewed journal __X_ Published in a peer-reviewed journal American Physical Society (2018) Volume 98, Issue 5 https://doi.org/10.1103/PhysRevB.98.054308 158 159 160 161 162 163 164 165 166 167 CHAPTER 12 SOLID-STATE LASER COOLING OF OPTICALLY LEVITATED PARTICLES Contribution of Authors and Co-Authors Manuscript in Chapter 12 Author: Demi St. John Contributions: Prepared material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Philip J. T. Woodburn: Contributions: Prepared material samples, designed and set up experimental apparatus, performed the measurements to acquire data, analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: David Atherton Contributions. Analyzed and interpreted results, generated figures, wrote and edited the manuscript. Co-Author: Charles Thiel Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Zeb Barber Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. Co-Author: Wm. Randall Babbitt Contributions: Analyzed and interpreted results, wrote and edited the manuscript, discussed results and implications. 168 Manuscript Information Demi St. John, Philip J. T. Woodburn, David Atherton, Charles Thiel, Zeb Barber, Wm. Randall Babbitt PROCEEDINGS OF SPIE Status of Manuscript: ___ Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-reviewed journal ____ Accepted by a peer-reviewed journal __X Published in a peer-reviewed journal Proc. SPIE 10723, Optical Trapping and Optical Micromanipulation XV, Vol. 10723 7 September 2018 DOI: 10.1117/12.2321194 169 170 171 172 173 174 175 176 177 CHAPTER 13 SUMMARY Studying rare earth ions in solid state crystal structures for fundamental discoveries and industrial application is an interesting and complex science. They can be studied to probe the quality of a crystal’s synthesis and fabrication process or used to store coherent information on the electron spins for quantum transduction. The REIs are used commercially for worldwide optical communication and the production of extreme wideband radio frequency sensors and signal processors. In this work the optical properties of REI doped insulators are the focus. Several characterization methods were used to determine critical aspects of REI doped powders and single crystals. High resolution spectroscopy was the main tool used to characterize the materials, using an array of coherent and conventional techniques. The spectral properties of triply ionized erbium, thulium, terbium and ytterbium were characterized at liquid helium temperatures. Linear and coherent techniques were used as sensitive methods to assess the effects of the mechanical, thermal, and chemical processes used to synthesize the materials. The optical spectral features of REIs dopants gave an insight into how the host material’s atomic structure holds the REIs. Static and dynamic defects are characterized using spectral properties, allowing a deeper understanding of the fundamental aspects of the REI and the host materials. The optical characterization is also used as a method to provide feedback to the synthesis and processing of the material, to improve the next crystal or powder growth. Material crystallinity and phase were determined using x-ray diffraction. Scanning electron microscopes were used to image the powder particle’s size, shape and growth structure. 178 Birefringence was used to quickly orient lower symmetry crystals by viewing the optical axes of the indicatrix. And birefringence images were also used to view strain and defects in single crystals. Chemical analysis was determined by glow discharge mass spectroscopy and laser ablation inductively coupled plasma mass spectrometry. To engineer a material, one can introduce similar ions into the lattice of a known or similar host. This can be done by gradually changing the chemistry in the case of YyLuxAl5O12 or 1%Eu, 0.01%Er:Y2SiO5 or by completely replacing an ion as Ga replaces Al in Y3Ga5O12 and Y3Al5O12 shown in Chapter 6 and Chapter 8. The synthesis and fabrication of the material was shown to be as important as the choice of material itself. Even single crystals such as Tm:YGG used in Chapter 6 can have significant differences depending on the parameters used in the Czochralski growth method, as discussed in Chapter 2. Materials that have industrial applications often have the production optimized enabling very high-quality material such as the single crystals of Er:YSO used in Chapter 5 as material for optical to radio frequency quantum transducer or the Yb:YVO4 characterized in Chapter 7 for next generation quantum memories built into a chip size device. High-quality material can also be produced in the lab with good technique and care. This was found to be especially true for the powders materials such as Tm:YAG, Er:LN and Tb:YAG presented in chapters 9, 10, and 11. We found that low levels of strain and defects in the crystal lattice that are not measurably detected by XRD or SEM analysis can still produce large variations in the observed low-temperature dynamics of the powders observed using SHB techniques, significantly impacting the performance of the powders in applications. Thus, SHB can serve as a quantitative characterization tool, complementing traditional techniques such as 179 XRD, SEM, or Raman scattering. Our results also demonstrate that mechanical and thermal treatment of REI doped crystals can reverse some detrimental effects of powder fabrication, such as minimizing the reduction in lifetime of nuclear spin states, in a surprisingly strong way, and in certain cases, the properties of the bulk material can be reached. Choosing the best host material is not simple. The number of available host materials are almost uncountable, but they can be put into a few very general classifications; crystals, glass, ceramics, and organics. 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