Cavity Quantum Optomechanics with Ultracold Atoms by Kater Whitney Murch B.A. (Reed College) 2002 M.A. (University of California, Berkeley) 2007 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: Professor Dan M. Stamper-Kurn, Chair Professor Irfan Siddiqi Professor Birgitta Whaley Spring 2008 The dissertation of Kater Whitney Murch is approved: Chair Date Date Date University of California, Berkeley Spring 2008 Cavity Quantum Optomechanics with Ultracold Atoms Copyright 2008 by Kater Whitney Murch 1 Abstract Cavity Quantum Optomechanics with Ultracold Atoms by Kater Whitney Murch Doctor of Philosophy in Physics University of California, Berkeley Professor Dan M. Stamper-Kurn, Chair A common goal of recent research is the elucidation and control over quantum mechanical behavior in ever-larger physical systems. In this thesis I present an alternative target for investigating the quantum motion of macroscopic bodies: the collective motion of an ultracold atomic gas trapped within a high-finesse Fabry-Perot optical cavity in the single- atom strong-coupling regime of cavity quantum electrodynamics (CQED). When ultracold atoms are trapped in the Lamb-Dicke regime, the cavity-mode structure selects a single collective degree of freedom that is at once actuated by the optical forces from cavity probe light and measured by the cavity’s optical properties. Dispersive optical bistability arising from collective motion of the atomic medium was observed. Measurement of the collective motion was subject to quantum measurement backaction by the quantum force fluctuations of the cavity optical field. The strength and spectrum of these backaction force fluctuations was measured by quantifying the cavity-light-induced heating rate of the intracavity atomic ensemble, finding quantitative agreement with the expected heating rate from quantum optical fluctuations. Dynamical phenomena in the optomechanical system were explored experimentally and theoretically. Quantum limited measurements are discussed and were explored experimentally. The application of these quantum limited measurements to precise measurements of the gravitational inverse-square law using betatron resonances is discussed. Professor Dan M. Stamper-Kurn Dissertation Committee Chair 2 i To all my teachers who broke the mold: Don Jolley, David Lapp, Nicholas Wheeler ii Contents List of Figures iv List of Tables vi 1 Introduction 3 1.1 Measurement and the quantum limit . 3 1.2 Cavity QED . 5 1.3 Optomechanics . 7 1.4 The next 100 pages . 8 2 Cavity-optomechanics with cold atoms 10 2.1 A model optomechanical system . 10 2.2 Many atom CQED . 12 2.3 Toward collective variables . 14 2.4 Normal modes of the system . 17 2.5 Comparison to traditional CQED: Cavity quantum optomechanics . 19 3 The experiment 21 3.1 The optical fields . 21 3.1.1 An imperfect cavity . 23 3.1.2 Cavity-QED parameters . 24 3.1.3 Photon detection efficiency . 24 3.2 The cavity lock chain . 25 3.2.1 The transfer cavity . 25 3.2.2 The science cavity . 28 3.2.3 Noise . 29 3.2.4 The temperature of photo-detection . 32 3.3 The FORT . 33 3.4 The atoms . 34 3.4.1 Condensation, collisions and the loitering at each lattice site . 34 3.5 Distribution of atoms in the lattice . 35 3.6 Experimental tricks . 37 3.6.1 Frequency sweeps . 37 3.6.2 Wait and see . 40 iii 3.6.3 Absorption imaging and time of flight . 40 4 Nonlinear optics from collective motion 42 4.1 Adiabatic collective motion . 44 4.2 The bistable potential . 47 4.3 Connection to experimental measures . 49 4.4 Granularity . 51 4.5 Nonlinearities at very low photon number . 52 5 Quantum measurement backaction 55 5.1 The two faced nature of light . 55 5.2 A model quantum measurement . 56 5.3 Backaction heating . 60 5.3.1 A quantum limited amplifier . 63 5.4 Heating from incoherent scattering . 66 5.5 Measuring backaction heating by the evaporative loss of trapped atoms . 67 5.5.1 Line rates . 68 5.5.2 Technical sources of heating . 70 5.5.3 Quantitative interpretation of the cavity line shape . 73 5.6 Off cavity-resonance heating . 76 5.7 Connection to quantum optics: an intracavity fluctuation bolometer . 79 6 Collective motion 83 6.1 “Kick and watch” . 84 6.2 The optomechanical frequency shift . 86 6.3 Amplification, damping, and saturation . 88 6.4 Toward quantum limited measurement . 89 6.4.1 Parameter estimation . 90 6.4.2 The “kick” . 94 6.4.3 Evolution . 95 6.5 Backaction induced phase diffusion . 101 6.6 The right left and center of cavity resonance . 103 6.7 The quantum–classical boundary: granularity revisited . 103 6.8 What? Who? Which way photons leave the cavity . 106 7 Betatron motion in the ultracold atom storage ring 109 7.1 Forming a storage ring for cold atoms . 111 7.2 Betatron resonances . 113 7.3 Modeling betatron resonances . 118 7.4 Dispersion Management . 118 8 A proposal to test the gravitational inverse-square law 129 Bibliography 134 iv List of Figures 1.1 Nature’s rulers . 4 1.2 Cavity QED . 5 2.1 The basic optomechanical system . 11 2.2 The spectrum of the many atom-cavity system. 13 2.3 The atoms-cavity system . 15 3.1 Schematic of the cavity lock chain . 26 3.2 Laser stabilization . 27 3.3 The Voigt profile . 29 3.4 Characterization of the science cavity lock . 32 3.5 Spatial dependence of the atom cavity coupling . 36 3.6 Absorption imaging versus cavity based atom counting . 36 3.7 Schematic of a typical experiment . 38 3.8 Two types of experiments . 39 3.9 Time-of-flight temperature measurement . 40 4.1 Asymmetric cavity lineshapes due to collective motion . 46 4.2 Dispersive bistability . 48 4.3 Bistable ringing . 49 4.4 Nonlinear and bistable cavity lineshapes . 50 4.5 Observation of collective adiabatic motion . 51 4.6 Optical nonlinearity at low photon number . 52 4.7 Nonlinearity withn ¯ ∼ 0.1 ............................ 53 5.1 Basics of a quantum measurement . 59 5.2 Quantum limited amplifiers . 65 5.3 Study of thermal and evaporative equilibration . 69 5.4 Temporal cavity lineshapes . 71 5.5 Line-time measurements . 72 5.6 Cavity-based observation of evaporative atomic losses . 75 5.7 Cavity-heating of the collective atomic mode . 76 5.8 Controlled dose experiment . 78 5.9 Branching ratios . 79 v 5.10 The fluctuation bolometer . 81 6.1 Kick and watch experiment . 84 6.2 The optomechanical frequency shift . 87 6.3 The nonlinear optomechanical frequency shift . 88 6.4 Study of data analysis techniques . 92 6.5 Amplitude estimates . 93 6.6 A classical kick for a quantum displacement . 96 6.7 Relevant timescales for measurement . 99 6.8 The kick and watch experiment . 101 6.9 Time resolved quantum measurement . 102 6.10 Spectrum of the cavity resonance . 104 6.11 Nonlinearity in the granular regime . 105 7.1 Forming a circular magnetic storage ring for ultracold atoms . 112 7.2 An ultracold-atom storage ring . 114 7.3 Computer simulation of a νz = 5 betatron resonance . 119 7.4 Basis of dispersion management with betatron resonances . 120 7.5 Stopbands for νr = 5 radial and νz = 5 axial betatron resonances. 121 7.6 Dispersion management of matter waves in a storage ring . 123 7.7 Matter wave dispersion at an axial betatron resonance . 124 7.8 Axial betatron motion . ..