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Quantum Degeneracy in an Attractive Bosonic System

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Quantum Degeneracy in an Attractive Bosonic System QUANTUM DEGENERACY IN AN ATTRACTIVE BOSONIC SYSTEM A DISSERTATION SUBMITTED TO THE DEPARTMENT OF PHYSICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Mingchang Liu September 2007 °c Copyright by Mingchang Liu 2008 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. (Alexander Fetter) 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. (Yoshihisa Yamamoto) Approved for the University Committee on Graduate Studies. iii Abstract iv Bose-Einstein condensate (BEC) is a new state of matter formed by boson cooled very close to absolute zero. Since the ¯rst realization of BEC in 1995, there have been tremendous amount of experimental and theoretical studies on this phenomenon. A lot of new observations have been made and have extended people's understanding about quantum mechanics. To achieve BEC state, one major approach is to use an e±cient magnetic trap as the working horse for evaporative cooling, which is one of the key steps. A well- designed trap with good performance can make an experiment relatively easy and can also make some "impossible" possible. In our experiment, we designed and im- plemented a millimeter-scale Io®e-Pritchard trap, Mini-Trap. This is not only a new instrument to achieve BEC but a novel concept since it is a di®erent solution from the traditional gigantic magnetic trap and micro-trap. It is well known that 7Li is hard to approach BEC state. Its features like small collisional cross section, negative scattering length and absence of sub-Doppler cool- ing, bring a huge challenge on the experimental side. Yet, with our new mini-trap design, we were able to realize quantum degeneracy for Lithium. In this thesis we also present a simple double well implementation and collisional dynamics in such a trap. The capability demonstrated by Mini-Trap for Lithium scales well for other alkalic particles. Our versatile design and compact setup proved to be a good choice as a platform for a portable interference measurement system. Lithium's unique feature of negative scattering length also makes a candidate for Schrodinger cat state. Schrodinger cat has been studied by photons, ions and superconductors. Atomic SchrÄodinger cat could be more interesting for research study and future applications because of the easy quantum control and extremely long coherence time. The research explores the characteristics for 7Li atoms in quantum degeneracy regime. And the study of the atomic SchrÄodinger Cat state is also another main subject for this thesis. In the ¯rst chapter, I will explain and describe the basic theory and techniques for BEC research, followed by the apparatus design and setup in the second chapter. The third chapter contains the experimental measurements for single well and double well v in quantum degeneracy regime. Finally, theoretical discussion, experimental setup and preliminary data will be discussed for atomic SchrÄodinger cat state in the forth chapter. vi Acknowledgement vii I want to take this opportunity to express my gratitude to those who have sup- ported, inspired, and encouraged me throughout my whole graduate study. It has been a great privilege to work Prof. Kasevich. He has been both an advisor and a friend to me. His continuous support and guidance is the key for me to succeed. Thanks to my lab mates, Olaf Mandel, Mike Minar, Nick Cizek, Ruquan Wang and Francesco Minardi, for their help and discussion during experiment. It is not desirable to work in a dark room day in and day out. However, these nice people has made it quite fun. Thanks to those who have given me a lot of insights and technical help, including Peter Hommelho®, Wei Li, Ari Tuchman, Grant Biedermann, Ken Takase, Catherine Kealhofer, Hui-Chun Chien, Xinan Wu, Nate Gemelke, Edina Sarajlic, Sheng-Wey Chiow. To our secretary, Ping Feng. Her hard work has made my life much easier in last ¯ve years. Many thanks to my colleagues in Prof. Kasevich's group, Prof. Chu's group and Prof. Bucksbaum's group and all my friends in Stanford. Thank you for being there for me. I am greatly grateful to my parents and my family back in China for their love, care and support. Thanks to Ron and Hanne,like my parents, they have been an important part of my life in last 5 years. Their love has been the sustaining power in both my life and my study. Last but not least, special thanks to my beautiful and thoughtful wife, for her belief in me and refuse to give me up. viii Contents Abstract iv Acknowledgement vii 1 Bose Einstein Condensation 1 1.1 A Brief History . 1 1.2 Ground State Properties in Harmonic Trap . 2 1.2.1 Bose Statistics . 2 1.2.2 Dilute Gas . 4 1.2.3 GPE equation . 4 1.3 Neutral atoms in magnetic ¯eld . 5 1.3.1 Hyper¯ne structure . 5 1.3.2 Interaction with external static magnetic ¯eld . 7 1.4 Laser Cooling . 8 1.4.1 Doppler Cooling . 8 1.4.2 Sub-Doppler Cooling . 10 1.5 The optical dipole trap . 10 1.6 Magnetic trapping . 12 1.7 Magneto-Optical Trap(MOT) . 13 1.8 Evaporative cooling . 15 1.8.1 How does evaporative cooling work . 16 1.8.2 Loss in a magnetic trap . 17 1.9 Quantum degeneracy for Lithium . 17 ix 1.9.1 Properties of Lithium . 18 1.9.2 single well and double well . 19 2 Experimental apparatus 20 2.1 Vacuum system . 20 2.1.1 A two-chamber system . 20 2.1.2 Oven Bake Out . 22 2.2 Laser System . 24 2.2.1 Frequency and power preparation . 24 2.2.2 Frequency lock loop . 26 2.2.3 Power redistribution for vacuum port . 26 2.2.4 Optical pumping . 29 2.3 Radio frequency system . 31 2.3.1 RF frequency generation . 31 2.3.2 Antenna . 31 2.4 Optical imaging . 32 2.4.1 Fluorescence Imaging . 32 2.4.2 Absorption Imaging . 33 2.5 Mini-Trap design and realization . 36 2.5.1 Di®erent magnetic trapping schemes . 36 2.5.2 Magnetic trap design consideration: scaling law . 40 2.5.3 Mini-Trap Realization . 41 2.6 Mini-Trap characterization . 46 2.6.1 Transfer between traps and experimental sequence . 47 2.6.2 Mini-Trap Lifetime Measurement . 54 2.6.3 Mini-Trapping Depth Measurement . 55 2.6.4 Mini-Trapping Frequency Measurement . 56 2.6.5 Temperature measurement with TOF . 61 2.6.6 Tweaking Trapping Properties . 62 2.7 Integrated data analysis environment . 64 2.8 What key features should be remembered for Mini-Trap? . 66 x 3 Quantum degeneracy of Lithium in Mini-Trap 67 3.1 Quantum Degeneracy in single Mini-Trap . 67 3.1.1 Metastable BEC with Attractive Interaction . 67 3.1.2 Experimental Results in simple harmonic trap . 68 3.1.3 Two-step time of flight . 72 3.2 Collisional experiment in a double well . 74 3.2.1 Dimple beam setup . 75 3.2.2 O®-line measurement of dimple beam size . 76 3.2.3 Dimple beam stability test . 78 3.2.4 Collisional experiment setup and results . 80 4 SchrÄodingerCat: alive or dead 84 4.1 SchrÄodingerCat . 84 4.2 Other SchrÄodingerCat experiments . 86 4.2.1 Mesoscopic quantum coherence in cavity QED . 87 4.2.2 Mesoscopic quantum coherence in a harmonic trap . 88 4.2.3 Macroscopic quantum coherence in superconductor . 89 4.3 Atomic SchrÄodingerCat . 91 4.3.1 Basic picture: Bose-Hubbard model in double well . 92 4.3.2 Numerical analysis . 96 4.3.3 Something about adiabatic process . 104 4.3.4 Detection: catch the cat . 105 4.4 Experimental Results . 109 4.4.1 Setup and procedure . 109 4.4.2 Observation and interpretation . 110 Bibliography 115 xi List of Tables xii List of Figures 1.1 Quantum statistics. (a) Boson; (b) Fermion . 2 1.2 7Li transition line . 6 1.3 Simple doppler cooling scheme . 8 1.4 MOT setup. (a) 3D con¯guration; (b) 1D cross section along Z axis. !0 is the atomic transition frequency and ! is the red-detuned MOT laser frequency. 14 1.5 RF forced evaporative cooling for trapped atoms . 15 2.1 Two chamber vacuum system. (a) trimetric view (b) top view. Pre- cooling chamber with heated Lithium source is green; Ion pumps are black and red; Science chamber is silver; Cross for current to feed in is orange ................................... 21 2.2 Main optical table . 25 2.3 Dye laser frequency lock loop. Saturation beam is coded with blue color and probing beam is coded in red. 27 2.4 Laser power distribute before getting into chamber . 28 2.5 Scheme for fluorescence imaging . 32 2.6 Scheme for absorption imaging . 33 2.7 A typical absorption imagine at RF=805Mhz . 35 2.8 Quadruple trap set up and e®ective magnetic ¯eld . 37 2.9 Standard Io®e-Pritchard trap setup and e®ective magnetic ¯eld . 39 2.10 Copper tube: main body of IP trap structure .
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