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The University of Chicago Bose-Einstein Condensates

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The University of Chicago Bose-Einstein Condensates THE UNIVERSITY OF CHICAGO BOSE-EINSTEIN CONDENSATES IN A SHAKEN OPTICAL LATTICE A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF PHYSICS BY LICHUNG HA CHICAGO, ILLINOIS JUNE 2016 Copyright © 2016 by Lichung Ha All Rights Reserved To my family and friends to explore strange new worlds, to seek out new life and new civilizations, to boldly go where no man has gone before. -Star Trek TABLE OF CONTENTS LIST OF FIGURES . viii LIST OF TABLES . x ACKNOWLEDGMENTS . xi ABSTRACT . xiv 1 INTRODUCTION . 1 1.1 Quantum simulation with ultracold atoms . 2 1.2 Manipulating ultracold atoms with optical lattices . 4 1.3 Manipulating ultracold atoms with a shaken optical lattice . 5 1.4 Our approach of quantum simulation with optical lattices . 6 1.5 Overview of the thesis . 7 2 BOSE-EINSTEIN CONDENSATE IN THREE AND TWO DIMENSIONS . 10 2.1 Bose-Einstein condensate in three dimensions . 10 2.2 Berezinskii-Kosterlitz-Thouless transition in two dimensions . 13 2.3 Gross-Pitaevskii Equation . 15 2.4 Bogoliubov excitation spectrum . 16 2.5 Superfluid-Mott insulator transition . 18 3 CONTROL OF ATOMIC QUANTUM GAS . 21 3.1 Feshbach resonance . 21 3.1.1 s-wave interactions . 22 3.1.2 s-wave scattering length . 22 3.2 Optical dipole potential . 25 3.3 Optical lattice . 27 3.3.1 Band structure . 29 3.3.2 Projecting the wavefunction in the free space . 31 3.4 Modulating the lattice . 32 3.4.1 Band hybridization . 32 3.4.2 Floquet model . 33 3.4.3 Heating in the shaken optical lattice . 34 4 PREPARING, PROBING AND MANIPULATING A CESIUM BEC . 38 4.1 Cesium atoms . 38 4.2 Hardware . 41 4.2.1 Vacuum system . 41 4.2.2 Diode lasers . 42 4.2.3 Optical dipole trap . 44 4.2.4 Control system . 46 4.3 Laser cooling . 47 v 4.3.1 Zeeman slowing . 47 4.3.2 Magneto-optical trap and optical molasses . 47 4.3.3 Degenerate Raman Sideband Cooling (dRSC) . 48 4.4 Evaporation . 50 4.5 Preparation of 2D quantum gases with an optical lattice . 51 4.6 Probing the atoms . 52 4.6.1 Absorption imaging . 52 4.6.2 Imaging system . 53 4.6.3 Modulation transfer function . 55 4.7 Optical lattice . 59 4.8 Projecting system . 61 4.8.1 Projection Bragg spectroscopy . 63 5 STRONGLY INTERACTING TWO-DIMENSIONAL BOSE GASES . 67 5.1 Introduction . 67 5.2 Experiment . 69 5.3 Equation of state measurement . 70 5.3.1 Determinating the chemical potential and temperature . 70 5.4 Extraction of the coupling constants . 72 5.5 Conclusion . 73 6 DIRECT OBSERVATION OF EFFECTIVE FERROMAGNETISM . 77 6.1 Introduction . 77 6.2 Experiment . 78 6.3 Observation of bifurcation . 80 6.4 Susceptibility measurement . 82 6.5 Observation of domain . 82 6.6 Domain reconstruction . 85 6.7 Domain correlation . 87 6.7.1 Correlation analysis . 89 6.8 Effective paramagnetic and ferromagnetic phases . 90 6.8.1 Initial velocity and effective field . 92 6.9 Quench dynamics . 93 7 ROTON-MAXON EXCITATION SPECTRUM . 96 7.1 Introduction . 96 7.2 Modified Bogoliubov Spectrum . 98 7.2.1 Phonon, maxon, and roton excitations . 100 7.2.2 Critical velocity by the Landau criteria . 101 7.3 Experimental configurations . 103 7.4 Roton dispersion measurement . 104 7.5 Critical velocity measurement . 107 vi 8 OUTLOOK . 112 8.1 Density order in a shaken optical lattice . 112 8.1.1 Structure factor and susceptibility in the 2D gas . 113 8.1.2 Density order in the 3D gas . 115 REFERENCES . 118 vii LIST OF FIGURES 2.1 Illustration of matter wave . 11 2.2 Zero temperature phase diagram of the Bose-Hubbard model . 20 3.1 Band structures . 30 3.2 Dependences on the lattice depth . 31 3.3 Dispersion calculation . 35 3.4 Scaling of the loss coefficient. 37 4.1 Cs scattering length . 39 4.2 Efimov . 40 4.3 Cs system . 41 4.4 The science chamber . 43 4.5 Trap depth . 45 4.6 Illustration of degenerate Raman sideband cooling . 49 4.7 Optical setup for creating the 2D gas . 51 4.8 Objective . 54 4.9 Transmission measurement of the 3-in-1 plate . 55 4.10 Modulation transfer function . 58 4.11 Illustration for the aberration . 59 4.12 Lattice phase modulation setup . 60 4.13 Calibration of the lattice depth . 61 4.14 Projection system . 62 4.15 Flat potential . ..
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