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High Contrast Measurements with a Bose-Einstein Condensate Atom Interferometer

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High Contrast Measurements with a Bose-Einstein Condensate Atom Interferometer High Contrast Measurements with a Bose-Einstein Condensate Atom Interferometer Billy Ian Robertson Experimental Quantum Optics and Photonics Group Department of Physics and SUPA University of Strathclyde A thesis presented in the fulfilment of the requirements for the degree of Doctor of Philosophy 2016 This thesis is the result of the authors original research. It has been composed by the author and has not been previously submitted for examination which has led to the award of a degree. The copyright of this thesis belongs to the author under the terms of the United Kingdom Copyright Acts as qualified by University of Strathclyde Regulation 3.50. Due acknowledgement must always be made of the use of any material contained in, or derived from, this thesis. Signed: Date: i Abstract Atom interferometry is a next-generation technique of precision measurement that can vastly outperform its optical analogue. These devices utilise the wave nature of atoms to make interferometric measurements of, for example, gravitational and magnetic fields, inertial effects, and the fine-structure constant. The main focus of this thesis is the creation of a general purpose atom interferometer in free space. We create a Bose-Einstein condensate of ∼105 87Rb atoms in a crossed-optical dipole trap. The atomic wavefunction is coherently manipulated using highly tuned pulses comprising off-resonant light that form our atom-optical elements. These atom optics are analogous to the beam splitters and mirrors in an optical interferometer. By controlling the timing and amplitude of the pulses we demonstrate the ability to excite specific momentum states with high efficiency. The tuned atom optics allows for the construction of an atom interferometer in free space. From this we can measure the recoil velocity of an 87Rb atom and calculate the value of the fine structure constant. We also demonstrate the measurement of magnetic field gradients using atom interferometry. A second method of data readout is also demonstrated, known as contrast inter- ferometry. This increases the rate at which information is obtained and decreases the measurement duration from a few hours to a few minutes. Within the vacuum chamber we also have a copper ring which form the basis of an AC coupled ring trap for atoms. The long term goal is to use this as a waveguide for atom interferometry and, whilst not the main focus of this thesis, we present some proof-of-principle type data demonstrating the ring trap. In addition we show the first Kapitza-Dirac splitting of a BEC within the waveguide which forms the first part of a guided atom interferometer. ii Acknowledgements I would like to express huge thanks to my primary supervisor, Paul Griffin. I really appreciate the time you have spent teaching and guiding me over the last few years, and how you always make time to help me. The way you can take seemingly complex physics and explain it simply and clearly is a great skill. Erling Riis, thank you for your inspiring conversations, wise words and support. The fact you still find time to visit the offices and labs, despite being head of the department, is very much appreciated. Thanks must go to Aidan Arnold, my unofficial third supervisor and the person who introduced me to Bose-Einstein condensates as an undergraduate student. Your expertise and suggestions in group meetings proved invaluable. To my colleague and friend Andrew MacKellar, I have very much enjoyed your company during my PhD and you’ve no doubt been a hugely positive influence on my work. I have learned many things from you, physics or otherwise. I thank greatly our previous post-doc Jonathan Pritchard and my PhD predecessor Aline Dinkelaker. Not only did you construct the excellent experiment foundation on which my work is based, but you also welcomed me into the photonics group and took the time to answer my questions and guide me in my early days. I am pleased to see a new PhD student, James Halket, join our experiment (if nothing else, it means I didn’t break it). I am excited to see what the future holds and I am confident you will produce some excellent data. My office mates, Andrew, Vicki, Rachel, and Jan. A wise man once proclaimed “best office ever!”, and I am tempted to agree. I feel very lucky that we get on so well, and I appreciate your company, advice, and support. When I first joined the group, we were a small band of physicists, but with the expansion of the the group to become the Experimental Quantum Optics and Photonics (EQOP) Group, we have greatly increased in number. I will not try to list all EQOP members past and present; there are so many, and in truth I fear I may forget someone. Therefore I will simply thank you as a group, and say I couldn’t have done it without you. My outside-of-work thanks go to family and friends. Mum and Dad, thank you for your endless love, support and encouragement. As far as I am concerned, my PhD is as much your achievement as it is mine; I am only here because of you and I feel very fortunate. iii Contents Abstract ii Acknowledgements iii Contents vi List of Figures vii 1 Introduction1 1.1 Research at the University of Strathclyde................ 1 1.2 Atom Interferometry .......................... 2 1.2.1 Atoms as Waves......................... 3 1.2.2 Advantages of Using Atoms .................. 4 1.2.3 Waveguides........................... 5 1.2.4 Cold Atoms, Bosons and Fermions............... 6 1.3 Ring Traps................................ 7 1.3.1 Optical Ring Traps....................... 7 1.3.2 RF Dressed Ring Traps..................... 7 1.3.3 Magnetic Ring Traps...................... 8 1.3.4 Our AC Coupled Ring Trap................... 8 1.4 Fine-Structure Constant......................... 8 1.4.1 Measurement of α ....................... 10 1.5 Thesis Outline.............................. 12 2 Cold Atoms & Quantum Gases 13 2.1 Cooling and Trapping of Neutral Atoms................ 13 2.1.1 Doppler Cooling ........................ 14 2.1.2 Sub-Doppler Cooling...................... 16 2.1.3 Magneto-Optical Traps..................... 18 2.1.4 Magnetic Trapping....................... 21 2.1.5 Optical Dipole Traps...................... 22 2.1.6 Radio Frequency Evaporative Cooling............. 23 2.1.7 Optical Evaporative Cooling.................. 25 2.2 Bose-Einstein Condensation ...................... 26 2.2.1 Phase-Space Density...................... 26 2.2.2 Bose Gas in a Harmonic Potential ............... 27 iv CONTENTS 2.2.3 Condensation in a Harmonic Potential............. 28 2.2.4 Condensate Fraction ...................... 29 3 Atom Interferometry and Splitting the Wavefunction 31 3.1 Bose-Einstein Condensates....................... 32 3.1.1 Coherence............................ 32 3.1.2 Momentum Spread....................... 34 3.2 Resonant Scattering........................... 35 3.3 Kapitza-Dirac Scattering ........................ 36 3.3.1 Single Pulses .......................... 37 3.3.2 Double Pulses.......................... 39 3.4 Composite Pulses for High Efficiency Splitting ............ 42 3.4.1 Blackman Pulses ........................ 44 3.4.2 Competing Methods ...................... 45 3.5 Atom Interferometer Model....................... 46 3.5.1 3-arm Interferometer Model .................. 46 3.5.2 2-arm Interferometer Model .................. 48 4 Experimental Setup 50 4.1 System.................................. 50 4.1.1 Vacuum System......................... 50 4.1.2 Glass Cells ........................... 51 4.1.3 Atom Source .......................... 51 4.1.4 Copper Ring........................... 52 4.1.5 Magnetic Coils ......................... 52 4.1.6 ECDL Lasers.......................... 53 4.1.7 Optics Setup........................... 54 4.1.8 Light-Induced Atomic Desorption............... 59 4.2 Experimental Sequence......................... 60 4.3 Interferometry Setup .......................... 69 4.3.1 Interferometry Laser Setup................... 69 4.3.2 Optical Control of Interferometer Sequence.......... 71 4.3.3 Contrast Interferometer Probe Beam.............. 74 4.3.4 Low Light Level Detection................... 75 5 Interferometry in Free Space 77 5.1 Optical Toolbox............................. 78 5.1.1 Lattice Depth Calibration.................... 78 5.1.2 First Order Atomic Beam Splitters............... 79 5.1.3 Second Order Atomic Beam Splitters ............. 82 5.1.4 Atomic Mirrors......................... 84 5.1.5 Efficiency and Limitations................... 87 v CONTENTS 5.1.6 Higher Order Splitting ..................... 88 5.2 Two-Arm Interferometer ........................ 89 5.3 Three-Arm Interferometer........................ 90 5.4 Magnetic Gradiometry ......................... 92 5.4.1 Method ............................. 95 5.4.2 Measurements.......................... 96 6 Contrast Interferometry 99 6.1 Difficulty ................................ 100 6.2 Avalanche Photodiode (APD) Detection . 101 6.2.1 First Detection ......................... 101 6.2.2 Further Analysis ........................ 103 6.2.3 APD Limitations ........................ 107 6.3 Single Photon Counting Module (SPCM) Detection . 108 6.3.1 Method of Detection ...................... 108 6.3.2 Measurements.......................... 108 7 AC Coupled Ring Trap 114 7.1 Theory.................................. 115 7.2 Thermal Atoms in the Ring Trap.................... 119 7.2.1 Loading from Dipole Trap ................... 121 7.2.2 Pendulum Modelling...................... 123 7.2.3 Kapitza-Dirac Splitting..................... 127 7.3 Limitations ..............................
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