TOC for Boris Braverman's Thesis (https://dspace.mit.edu/handle/1721.1/120364)

BravermanThesis2018.tex

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  pdftitle={Cavity Quantum Electrodynamics with Ensembles of Ytterbium-171},
  pdfauthor={Boris Braverman},
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\bookmark[page=3,level=0]{Abstract}
\bookmark[page=5,level=0]{Acknowledgements}
\bookmark[page=7,level=0]{Contents}
\bookmark[page=13,level=0]{List of Figures}
\bookmark[page=29,level=0]{List of Tables}
\bookmark[page=31,level=0]{1 Introduction}
  \bookmark[page=31,level=1]{1.1 Optical Lattice Clocks}
  \bookmark[page=39,level=1]{1.1.1 Systematic Errors in Optical Lattice Clocks}
  \bookmark[page=41,level=1]{1.2 Fundamental Physics with Precision Atomic Measurements}
  \bookmark[page=43,level=1]{1.3 Quantum Metrology and Squeezing}
  \bookmark[page=46,level=1]{1.3.1 Previous Work on Spin Squeezing}
  \bookmark[page=48,level=1]{1.4 Thesis Outline}
\bookmark[page=51,level=0]{2 Cavity Quantum Electrodynamics with Ytterbium}
  \bookmark[page=52,level=1]{2.1 Ytterbium}
  \bookmark[page=54,level=1]{2.1.1 Key Properties of Ytterbium-171}
  \bookmark[page=56,level=1]{2.2 Atom-Light Interactions in Cavities}
    \bookmark[page=60,level=2]{2.2.1 Simulating a Cavity with Lossy Mirrors by a Lossless Cavity with Additional Loss}
    \bookmark[page=62,level=2]{2.2.2 Modeling Light Polarization and Cavity Birefringence}
  \bookmark[page=64,level=1]{2.3 Ytterbium Atoms in a Cavity}
    \bookmark[page=64,level=2]{2.3.1 Atomic Response in a Magnetic Field}
    \bookmark[page=70,level=2]{2.3.2 Approximate Atomic Response for Typical Experimental Configurations}
    \bookmark[page=73,level=2]{2.3.3 Condition for Low Saturation Regime}
  \bookmark[page=74,level=1]{2.4 Cavity QED Simulation Examples}
    \bookmark[page=74,level=2]{2.4.1 Cavity QED Simulations with Zero Magnetic Field}
    \bookmark[page=76,level=2]{2.4.2 Cavity QED Simulations of Response to Probing}
    \bookmark[page=78,level=2]{2.4.3 Cavity QED Simulations with Magnetic Field Along Cavity Axis}
    \bookmark[page=81,level=2]{2.4.4 Cavity QED Simulations of Atomic Coherence Effects}
  \bookmark[page=82,level=1]{2.5 Classical and Quantum Fisher Information}
    \bookmark[page=84,level=2]{2.5.1 Fisher Information in States of Light}
  \bookmark[page=88,level=1]{2.6 Measurement of the Atomic State}
    \bookmark[page=88,level=2]{2.6.1 Fisher Information of Cavity Light About the Atomic State}
    \bookmark[page=90,level=2]{2.6.2 Dispersive Atom Counting}
    \bookmark[page=93,level=2]{2.6.3 On-Resonance Atom Counting}
    \bookmark[page=94,level=2]{2.6.4 Two-Color Probing}
  \bookmark[page=99,level=1]{2.7 Back-Action of Probing Light on Atoms}
    \bookmark[page=99,level=2]{2.7.1 Atom Phase Shift by Probing Light}
    \bookmark[page=101,level=2]{2.7.2 Spin Squeezing by Cavity Feedback}
    \bookmark[page=103,level=2]{2.7.3 Interaction-Based State Readout}
  \bookmark[page=104,level=1]{2.8 Spin Squeezing and Metrological Gain}
    \bookmark[page=106,level=2]{2.8.1 Measurement Variances for Squeezed States}
    \bookmark[page=110,level=2]{2.8.2 Squeezed Clock Stability}
    \bookmark[page=115,level=2]{2.8.3 Ultimate Clock Performance with Entangled States}
  \bookmark[page=117,level=1]{2.9 Beyond Spin Squeezing}
    \bookmark[page=117,level=2]{2.9.1 Spin Carving}
    \bookmark[page=119,level=2]{2.9.2 Schrödinger Cat States and Beyond by Unitary Squeezing}
\bookmark[page=125,level=0]{3 Experimental Cavity}
  \bookmark[page=126,level=1]{3.1 Theory of Free-Space Optical Cavities}
    \bookmark[page=130,level=2]{3.1.1 Symmetric Cavities}
    \bookmark[page=131,level=2]{3.1.2 Asymmetric Cavities}
    \bookmark[page=132,level=2]{3.1.3 Limits to Finesse for Cavities with Small Waists}
  \bookmark[page=133,level=1]{3.2 Key Parameters of Experimental Cavity}
  \bookmark[page=135,level=1]{3.3 Characterization of High Reflectivity Mirrors and High Finesse Cavities}
    \bookmark[page=135,level=2]{3.3.1 Mirror Transmission Measurement}
    \bookmark[page=136,level=2]{3.3.2 Cavity Free Spectral Range Measurement}
    \bookmark[page=137,level=2]{3.3.3 Cavity Finesse Measurement}
  \bookmark[page=141,level=1]{3.4 Construction of Experimental Cavity}
    \bookmark[page=141,level=2]{3.4.1 Experimental Cavity Structure}
    \bookmark[page=143,level=2]{3.4.2 Experimental Cavity Assembly and Alignment Procedure}
    \bookmark[page=145,level=2]{3.4.3 Micromirror Fabrication and Characterization}
    \bookmark[page=149,level=2]{3.4.4 Dielectric Mirror Coating}
    \bookmark[page=150,level=2]{3.4.5 Etching of Dielectric Coatings}
    \bookmark[page=154,level=2]{3.4.6 Deposition of SiO2 and Annealing of Micromirrors}
    \bookmark[page=155,level=2]{3.4.7 Mitigation of Clock Shifts Due to Electric Fields}
    \bookmark[page=158,level=2]{3.4.8 Micromirror Testing and Selection}
    \bookmark[page=159,level=2]{3.4.9 Cavity Properties Versus Alignment}
    \bookmark[page=164,level=2]{3.4.10 Epoxying of Cavity Components}
    \bookmark[page=168,level=2]{3.4.11 Wiring of Experimental Cavity}
    \bookmark[page=172,level=2]{3.4.12 Insertion of Cavity Into Vacuum Chamber}
    \bookmark[page=173,level=2]{3.4.13 Final Adjustment of Experimental Cavity Alignment}
  \bookmark[page=173,level=1]{3.5 Characterization of Experimental Cavity}
    \bookmark[page=173,level=2]{3.5.1 Finesse of Higher Order Transverse Modes}
    \bookmark[page=174,level=2]{3.5.2 Coupling of Cavity Light to Single-Mode Fiber}
    \bookmark[page=176,level=2]{3.5.3 Temperature Stabilization of Experimental Cavity}
    \bookmark[page=181,level=2]{3.5.4 Tuning of Alignment by Temperature}
    \bookmark[page=183,level=2]{3.5.5 Tuning of FSR by Temperature}
    \bookmark[page=184,level=2]{3.5.6 Cavity Frequency Stabilization}
    \bookmark[page=185,level=2]{3.5.7 Cavity Birefringence}
    \bookmark[page=190,level=2]{3.5.8 Cavity Photothermal Effects Due to Absorption in Dielectric Coatings}
\bookmark[page=193,level=0]{4 Apparatus}
  \bookmark[page=193,level=1]{4.1 Vacuum System}
    \bookmark[page=194,level=2]{4.1.1 Ytterbium Oven}
    \bookmark[page=196,level=2]{4.1.2 Heated Window}
    \bookmark[page=198,level=2]{4.1.3 Vacuum Pumps}
    \bookmark[page=199,level=2]{4.1.4 Vacuum Chamber Bake}
  \bookmark[page=201,level=1]{4.2 Lasers}
    \bookmark[page=201,level=2]{4.2.1 399 nm Laser System}
    \bookmark[page=202,level=2]{4.2.2 556 nm Laser System}
    \bookmark[page=210,level=2]{4.2.3 578 nm Clock Laser}
    \bookmark[page=214,level=2]{4.2.4 759 nm Magic Wavelength Optical Lattice Laser}
    \bookmark[page=220,level=2]{4.2.5 Repumping Lasers}
  \bookmark[page=221,level=1]{4.3 Reference Cavities for Laser Stabilization}
    \bookmark[page=222,level=2]{4.3.1 Commercial Ultrastable Cavity}
    \bookmark[page=225,level=2]{4.3.2 Homebuilt 4-Axis Reference Cavity}
  \bookmark[page=227,level=1]{4.4 Magnetic Field Control}
    \bookmark[page=227,level=2]{4.4.1 MOT Coils}
    \bookmark[page=229,level=2]{4.4.2 Magnetic Bias Field Coils}
    \bookmark[page=230,level=2]{4.4.3 Fast AC Magnetic Coil}
  \bookmark[page=230,level=1]{4.5 Optics Setup}
    \bookmark[page=230,level=2]{4.5.1 MOT Optics}
    \bookmark[page=232,level=2]{4.5.2 Cavity Coupling Optics}
    \bookmark[page=236,level=2]{4.5.3 Imaging Optics}
  \bookmark[page=236,level=1]{4.6 Experimental Control System}
  \bookmark[page=239,level=1]{4.7 Data Analysis}
    \bookmark[page=239,level=2]{4.7.1 Real-Time Data Analysis}
    \bookmark[page=240,level=2]{4.7.2 Off-Line Data Analysis}
\bookmark[page=241,level=0]{5 Results}
  \bookmark[page=241,level=1]{5.1 Atom Cooling and Trapping}
    \bookmark[page=242,level=2]{5.1.1 Two-Color MOT}
    \bookmark[page=243,level=2]{5.1.2 MOT Imaging and Position Measurement}
  \bookmark[page=246,level=1]{5.2 Loading of Atoms into Optical Lattice}
    \bookmark[page=246,level=2]{5.2.1 Continuous Non-Destructive Atom Counting}
    \bookmark[page=248,level=2]{5.2.2 Loading Efficiency for Different Lattice Powers and MOT-Mirror Distances}
    \bookmark[page=250,level=2]{5.2.3 Lattice Loading Near the Micromirror Surface}
    \bookmark[page=251,level=2]{5.2.4 Lattice Modulation Spectroscopy}
    \bookmark[page=251,level=2]{5.2.5 Atom Temperature Measurement}
  \bookmark[page=252,level=1]{5.3 Optical Pumping}
  \bookmark[page=254,level=1]{5.4 Rabi Flopping of 171Yb Nuclear Spin}
  \bookmark[page=255,level=1]{5.5 Ramsey Spectroscopy with 171Yb Nuclear Spin}
    \bookmark[page=256,level=2]{5.5.1 Ramsey Spectroscopy with Spin Echo}
  \bookmark[page=256,level=1]{5.6 AC Stark Shift by Probing Light}
    \bookmark[page=258,level=2]{5.6.1 Dependence of Phase Shift on Lattice Depth}
  \bookmark[page=260,level=1]{5.7 Atom Number Measurement}
    \bookmark[page=260,level=2]{5.7.1 Atom Number Measurement by Chirp}
    \bookmark[page=263,level=2]{5.7.2 Observation of Measurement-Based Spin Squeezing}
  \bookmark[page=265,level=1]{5.8 Cavity Feedback Spin Squeezing}
\bookmark[page=269,level=0]{6 Conclusion and Outlook}
\bookmark[page=271,level=0]{A. 3-D Printed Optical Shutters}
\bookmark[page=277,level=0]{B. Four-Axis Reference Cavity for Laser Stabilization}
  \bookmark[page=277,level=1]{B.1 Reference Cavity Design}
    \bookmark[page=278,level=2]{B.1.1 Temperature Stabilization of Reference Cavity}
  \bookmark[page=281,level=1]{B.2 Design Considerations for Stable Reference Cavities}
\bookmark[page=285,level=0]{C. Electronics}
  \bookmark[page=285,level=1]{C.1 Real-Time Atom Counting Circuit}
  \bookmark[page=288,level=1]{C.2 Coil Current Driver for Large AC Magnetic Fields}
  \bookmark[page=293,level=1]{C.3 Four-Point Measurement Temperature Controller}
\bookmark[page=295,level=0]{D. Maximum Likelihood Estimation and Fitting}
  \bookmark[page=295,level=1]{D.1 Fitting Probability Distributions with MLE}
    \bookmark[page=299,level=2]{D.1.1 Likelihood Function and Goodness of Fit}
  \bookmark[page=300,level=1]{D.2 MLE Fitting of Gaussian and Lorentzian Distributions}
  \bookmark[page=302,level=1]{D.3 MLE Weighted Averaging of Data}
  \bookmark[page=303,level=1]{D.4 Classical Fisher Information and the Cramér-Rao Bound}
\bookmark[page=307,level=0]{List of Acronyms}
\bookmark[page=313,level=0]{Bibliography}

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