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Atom Interferometry in an Optical Cavity by Matthew Jaffe a Dissertation Submitted in Partial Satisfaction of the Requirements F

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Atom Interferometry in an Optical Cavity by Matthew Jaffe a Dissertation Submitted in Partial Satisfaction of the Requirements F Atom interferometry in an optical cavity by Matthew Jaffe A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Associate Professor Holger Müller, Chair Associate Professor Norman Yao Professor Karl van Bibber Fall 2018 Atom interferometry in an optical cavity Copyright 2018 by Matthew Jaffe 1 Abstract Atom interferometry in an optical cavity by Matthew Jaffe Doctor of Philosophy in Physics University of California, Berkeley Associate Professor Holger Müller, Chair Matter wave interferometry with laser pulses has become a powerful tool for precision measurement. Optical resonators, meanwhile, are an indispensable tool for control of laser beams. We have combined these two components, and built the first atom interferometer inside of an optical cavity. This apparatus was then used to examine interactions between atoms and a small, in-vacuum source mass. We measured the gravitational attraction to the source mass, making it the smallest source body ever probed gravitationally with an atom interferometer. Searching for additional forces due to screened fields, we tightened constraints on certain dark energy models by several orders of magnitude. Finally, we measured a novel force mediated by blackbody radiation for the first time. Utilizing technical benefits of the cavity, we performed interferometry with adiabatic passage. This enabled new interferometer geometries, large momentum transfer, and in- terferometers with up to one hundred pulses. Performing a trapped interferometer to take advantage of the clean wavefronts within the optical cavity, we performed the longest du- ration spatially-separated atom interferometer to date: over ten seconds, after which the atomic wavefunction was coherently recombined and read out as interference to measure gravity. This work demonstrates the feasibility and utility of bringing a cavity to atom interferometry. i Contents Contents i List of Figures iv List of Tables vii 1 Introduction 1 1.1 Interferometry and matter waves ........................ 1 1.2 Outline of thesis ................................. 3 2 Atom interferometry: background and theory 4 2.1 Overview of an atom interferometer ....................... 4 2.2 Free evolution and the path integral formulation ................ 5 2.3 Atom-laser interactions .............................. 11 2.3.1 Raman transitions: the system ..................... 11 2.3.2 Solving the equation ........................... 12 2.3.3 Laser phases in an interferometer .................... 19 2.3.4 Bragg diffraction ............................. 23 2.4 The canonical example: gravity ......................... 24 2.5 Adding a perturbation .............................. 26 2.5.1 Other phase shifts ............................ 27 2.6 Optical resonators ................................ 28 3 Experimental apparatus 35 3.1 Vacuum chamber ................................. 35 3.2 The science cavity ................................ 36 3.3 Laser system ................................... 40 3.3.1 Trap and cooling lasers .......................... 40 3.3.2 Interferometry lasers and lock schemes ................. 45 3.4 Atom source and preparation .......................... 46 3.5 Additional details ................................. 53 3.5.1 Experimental control ........................... 53 ii 3.5.2 Raman signal generation ......................... 53 3.5.3 Inertial stabilization ........................... 54 4 Interferometry in the cavity 73 4.1 Cavity challenges ................................. 73 4.2 Cavity benefits .................................. 75 4.3 Raman pulses in a cavity ............................. 76 4.3.1 Finite-sized cloud in a finite-sized beam ................ 76 4.3.2 Rabi frequency and ac Stark shift with multiple beams ........ 81 4.4 Interferometry and results ............................ 89 5 Gravity and dark energy with a source mass 94 5.1 What is dark energy, and how do we know it’s there? ............. 94 5.2 Quintessence: scalar fields as dark energy .................... 97 5.2.1 Motivation ................................ 97 5.2.2 A force arises (and is screened) ..................... 98 5.2.3 The chameleon mechanism ........................ 99 5.2.4 Chameleon hunting ............................ 100 5.3 Source mass and interferometer geometry .................... 103 5.4 Gravitational attraction measurement ...................... 106 5.5 Constraints on screened fields .......................... 109 5.5.1 Symmetrons ................................ 110 5.5.2 Exclusions ................................. 111 5.6 Systematic effects ................................. 113 6 Blackbody radiation: a new force mediator 120 6.1 A force due to blackbody radiation ....................... 120 6.1.1 Qualitatively ............................... 120 6.1.2 Quantitatively .............................. 122 6.2 Measuring the blackbody radiation force .................... 123 6.2.1 Modeling and predictions ........................ 123 6.2.2 Measurements ............................... 126 7 Spin-dependent kicks for adiabatic passage in atom interferometers 135 7.1 Adiabatic passage ................................. 135 7.1.1 The basics ................................. 135 7.1.2 Constructing a pulse ........................... 138 7.1.3 Applying the pulse to an atom ..................... 139 7.2 Splitting the beamsplitter ............................ 143 7.3 SDK interferometry ................................ 146 7.3.1 SDK advantages ............................. 147 7.3.2 The dynamic phase ............................ 150 iii 7.3.3 Large momentum transfer ........................ 151 7.3.4 Single source gradiometer ........................ 152 7.3.5 Looped interferometer for ac signals .................. 153 7.4 Real world issues ................................. 155 7.4.1 Doppler separation ............................ 155 7.4.2 More dynamic phase ........................... 155 7.4.3 Dynamic phase cancellation ....................... 160 7.5 Summary ..................................... 162 8 Lattice atom interferometry 163 8.1 Trapped atom interferometer in an optical lattice ............... 164 8.1.1 Phase calculation ............................. 165 8.2 Far-detuned laser system ............................. 168 8.2.1 Widely-tunable locking scheme ..................... 168 8.3 Immunity to vibrations .............................. 174 8.3.1 The framework .............................. 174 8.3.2 Comparison of lattice AI and Mach-Zehnder vibration sensitivities .. 180 8.4 Bloch oscillations ................................. 182 8.5 Experimental implementation and results .................... 186 8.5.1 Lifetime limitations for long holds .................... 186 8.5.2 Contrast oscillations ........................... 189 8.5.3 Preliminary results ............................ 191 8.6 Summary ..................................... 192 9 Future prospects 194 9.1 Short term ..................................... 194 9.2 Medium term ................................... 195 9.3 Longer term .................................... 196 9.3.1 New directions .............................. 196 Bibliography 201 iv List of Figures 2.1 Simple Interferometer ................................ 9 2.2 Three-level Raman system .............................. 11 2.3 Mach-Zehnder schematic ............................... 21 2.4 Bragg diffraction ................................... 23 2.5 Mach-Zehnder light pulse interferometer ...................... 24 2.6 Basic optical resonator ................................ 28 2.7 Optical gain in matched optical resonators ..................... 31 3.1 The vacuum chamber ................................. 36 3.2 Schematic of the science cavity ........................... 37 3.3 Free spectral range measurement .......................... 38 3.4 Optical components ................................. 41 3.5 Hyperfine structure of the D2 line in cesium .................... 42 3.6 Locking scheme .................................... 42 3.7 Generation and delivery of MOT light ....................... 44 3.8 Science cavity lock scheme .............................. 45 3.9 Raman sideband cooling ............................... 49 3.10 Microwave transfer to the magnetically insensitive state. ............. 50 3.11 Atom launch ..................................... 51 3.12 Launched atom clouds ................................ 52 3.13 Raman phase lock loop ................................ 54 3.14 Passive vibration isolation .............................. 55 3.15 Basic Control Loop .................................. 56 3.16 Simple Bode plots .................................. 57 3.17 Simple Nyquist plots ................................. 60 3.18 Vibration stabilization control loop ......................... 61 3.19 Mechanical response G(s) to vibrations ....................... 63 3.20 Op amp lag compensator ............................... 65 3.21 Controller transfer function H(s) .......................... 65 3.22 Controller circuit schematic ............................. 66 3.23 Open loop transfer function Nyquist and Bode plots ............... 66 3.24 Closed-loop transfer function Bode plots ...................... 67 v 3.25 Performance of the active vibration stabilization .................. 68 3.26 Interferometer vibration noise ............................ 69 3.27 Tilt stabilization loop ...............................
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