BOSE-EINSTEIN CONDENSATION AND MACROSCOPIC INTERFERENCE WITH ATOMIC TUNNEL ARRAYS a dissertation submitted to the department of applied physics and the committee on graduate studies of stanford university in partial fulfillment of the requirements for the degree of doctor of philosophy Brian Philip Anderson January 2000 c Copyright 2000 by Brian Philip Anderson All Rights Reserved ii I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Mark Kasevich (Principal Adviser) I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Steven Chu (Physics and Applied Physics) I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Alexander Fetter (Physics and Applied Physics) Approved for the University Committee on Graduate Studies: iii Abstract Bose-Einstein condensation in a dilute vapor of magnetically trapped 87Rb was achieved, and the condensed atoms were used to observe de Broglie-wave interfer- ence due to atom tunneling between the barriers of an array of traps. The condensed atoms were loaded into a vertically-oriented one-dimensional optical lattice formed by a retro-reflected laser beam, creating the trap array. In the limit of negligible interactions between atoms, the energy difference between adjacent array sites was determined by the gravitational potential energy shift between the sites. This energy difference initiated an oscillating atom mass current similar to an electric current in the ac Josephson effect for two coupled superconductors. In the optical lattice, de Broglie-wave interference occurred between atoms in localized lattice states, and the interference was observed as a train of falling pulses of atoms. In a separate experiment, using a dilute vapor of lithium, enhanced loading of a 7Li magneto-optic trap with spectrally-broadened cooling and trapping light was demonstrated. By placing the Li oven nozzle near the trap, the Li atoms could be efficiently captured from an atomic beam without using a pre-cooling stage. The trapped atoms were transferred into a three-dimensional optical lattice, formed by four intersecting and interfering beams of far-off-resonant laser light, and adiabatic cooling and velocity selection in three dimensions was demonstrated. iv Acknowledgements I sincerely thank my advisor, Mark Kasevich, for his guidance and suggestions during the course of this work. His exceptional insight and creativity have been indispensable, and I am privileged to have had the opportunity to work closely with him for more than six years. I also thank my colleagues for assistance with various projects and for many beneficial discussions, especially Todd Gustavson, Jeff McGuirk, Brent Young, Heun Jin Lee, and Alastair Sinclair. I owe special thanks to Masami Yasuda for help with data collection in the final stages of this work, and for keeping the research alive while I worked on this dissertation; to Ken Sherwin for help with numerous diverse tasks at Stanford; and to Randy Hulet for initially nudging me in the direction of Stanford University. This work was made much more fulfilling by the many fantastic people that have helped cultivate my life beyond the lab. I have particularly enjoyed innumerable interesting and humorous conversations and enterprises with Todd Gustavson, as well as the company of Doug Smith during countless hikes and adventures in California’s great outdoors. I am also especially appreciative of close friendships with Jennifer Breitzmann, Monica Davis, Kristin Gustavson, and Donnasue Graesser, who have provided substance to my life as a graduate student. I am deeply grateful to my family, especially my parents, for their ceaseless and unlimited love and support. I particularly thank my aunt and uncle, Dorothy and Bill Farrell, and my cousins, Billy and Carla, Petrice, and Shannon, for helping to make my time in New Haven enjoyable, warm, and memorable. v Contents Abstract iv Acknowledgements v 1 Introduction 1 1.1 Contemporary atomic physics ...................... 1 1.2 Format of this dissertation ........................ 3 2 Cooling and trapping neutral atoms 6 2.1 Background ................................ 6 2.1.1 Atoms in external fields ..................... 6 2.1.2 Laser cooling ........................... 7 2.1.3 Bose-Einstein condensation ................... 7 2.2 Atom-photon interactions ........................ 7 2.2.1 The two-level atom ........................ 7 2.2.2 Doppler cooling .......................... 11 2.2.3 Beyond the two-level atom model ................ 12 2.2.4 Optical pumping ......................... 12 2.2.5 Lithium and Rubidium ...................... 13 2.3 Magneto-optic traps ........................... 13 2.4 Optical traps ............................... 16 2.4.1 Dipole forces ........................... 16 2.4.2 Optical lattices .......................... 17 2.5 Magnetic traps .............................. 18 vi 2.5.1 Spherical-quadrupole trap .................... 19 2.5.2 Time-averaged orbiting potential trap .............. 20 2.6 Evaporative cooling ............................ 22 2.7 Bose-Einstein condensation ........................ 25 2.8 Consolidation of techniques ....................... 28 3 Enhanced loading of a 7Li magneto-optic trap 29 3.1 Motivation ................................. 29 3.2 Direct loading from an atomic beam .................. 30 3.2.1 Experimental considerations ................... 31 3.2.2 Trap capture velocity ....................... 32 3.3 Experimental setup ............................ 33 3.4 Spectrally-broadened laser light ..................... 36 3.5 Trap images ................................ 41 3.6 Summary ................................. 41 4 Trapping 7Li in an optical lattice 44 4.1 Motivation ................................. 44 4.2 A far-detuned optical lattice for Li ................... 45 4.3 Experiment ................................ 46 4.3.1 Apparatus ............................. 46 4.3.2 Experimental sequence ...................... 51 4.3.3 Trap loss .............................. 53 4.4 Velocity selection and adiabatic cooling ................. 55 4.5 Summary ................................. 56 5 Light-induced atom desorption 58 5.1 Motivation: BEC ............................. 58 5.2 Vapor cell magneto-optic traps ...................... 59 5.3 Experiment ................................ 61 5.3.1 Lasers ............................... 62 5.3.2 Rb vapor cell ........................... 62 vii 5.3.3 Light-assisted losses ........................ 63 5.3.4 The Rb MOT ........................... 63 5.3.5 White light source ........................ 64 5.3.6 Measurements ........................... 64 5.4 Modeling the effects of the white light source .............. 67 5.5 Assessing the gains of LIAD ....................... 73 5.5.1 Observations ........................... 73 5.5.2 Extension of the technique to other atomic species ....... 73 5.5.3 Caution .............................. 73 5.6 Summary ................................. 74 6 Bose-Einstein condensation of 87Rb 75 6.1 Motivation ................................. 75 6.2 Experimental approach to BEC ..................... 76 6.3 Apparatus ................................. 76 6.3.1 Lasers ............................... 76 6.3.2 Vacuum system .......................... 77 6.3.3 DC magnetic-field bias coils ................... 79 6.3.4 Spherical-quadrupole field coils ................. 80 6.3.5 TOP field coils .......................... 82 6.3.6 RF coil ............................... 84 6.3.7 Timing system .......................... 84 6.4 Sequence .................................. 84 6.4.1 Dark MOT ............................ 86 6.4.2 Transfer to magnetic trap .................... 86 6.4.3 TOP-induced evaporative cooling ................ 88 6.4.4 Magnetic trap imaging ...................... 90 6.4.5 RF evaporative cooling: reaching the BEC threshold ..... 92 6.5 BEC measurements and images ..................... 94 6.6 BEC results ................................ 98 6.7 On-resonance dark-ground imaging ................... 101 viii 6.8 Calibrations, systematic errors, and measurement uncertainties .... 102 6.8.1 Imaging system .......................... 102 6.8.2 Magnetic fields .......................... 107 6.8.3 Laser light ............................. 108 6.8.4 Random noise and fluctuations ................. 109 6.8.5 Error analysis ........................... 109 6.8.6 Limitations ............................ 109 6.9 Apparatus improvements ......................... 111 6.10 Summary ................................. 113 7 Atomic tunnel arrays 114 7.1 Introduction ................................ 114 7.2 Josephson effects in superconductors .................. 114 7.3 General approach ............................. 116 7.4 Atomic tunnel array: theory ....................... 117 7.4.1 Model system ........................... 117 7.4.2 Quantum calculation ....................... 120 7.4.3 Interband tunneling ........................ 122 7.5 Trapping a BEC in an optical lattice .................. 123 7.6 Atomic tunnel array: observations .................... 124 7.6.1 Low Intensity lattice ....................... 124 7.6.2 High-intensity lattice ....................... 128 7.6.3 Hold and Release ........................