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Simulating Transport Through Quantum Networks in the Presence of Classical Noise Using Cold Atoms by Christopher Gill

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Simulating Transport Through Quantum Networks in the Presence of Classical Noise Using Cold Atoms by Christopher Gill Simulating transport through quantum networks in the presence of classical noise using cold atoms by Christopher Gill A thesis submitted to The University of Birmingham for the degree of DOCTOR OF PHILOSOPHY Ultracold Atoms Group School of Physics and Astronomy College of Engineering and Physical Sciences The University of Birmingham Sep 2016 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. Abstract In work towards the development and creation of practical quantum devices for use in quantum com- puting and simulation, the importance of long lived coherence is key to the advantages offered over classical systems. Isolation from environmental sources of decoherence is of integral importance to such platforms. Recent experiments of biological systems seem to indicate the existence of certain structures that utilise the decohering effects of their surrounding environments to enhance performance. In this thesis, we present a novel experimental set-up used to simulate the effect of decoherence-enhanced systems by mapping the energy level structure of laser cooled Rubidium 87 atoms interacting with electro- magnetic fields to a quantum network of connected sites. Classical noise is controllably added to the states to create a tunable system to explore these effects. We present the design and implementation of the system, with results of several technical aspects, along with initial work on the effect of the applied noise on transport through the network. We present a key result that transport through the network is non-trivially enhanced by the presence of an optimum amplitude of noise, pointing to the interplay between the coherent nature of the quantum system and the decoherence provided by the noise. ACKNOWLEDGEMENTS I would like to acknowledge the following people: Person Reason Dr. Vincent Boyer For being simply a fantastic supervisor and mentor. For his overall support and helping me with the wonderful world Dr. Plamen Petrov of UHV technology. For joining the experiment in my final year and putting up with Andy White the stressful pace of learning an experiment built from the ground up with somewhat less than perfect documentation. The Nuclear Physics PhD For being reliable lunch companions and great friends. Students et al. The Birmingham For sharing a lab with me for several years and allowing me to iSense Team test the very limits of `borrowing' equipment. The Birmingham For the vibrant group environment and many tech-talks. Cold Atoms Group Louise For putting up with occasionally playing second fiddle to my PhD. My Parents For the tremendously positive impact they have had on my life. CONTENTS 1 Overview 1 1.1 Background . .2 1.1.1 Biological Motivation . .2 1.1.2 Quantum Networks . .3 1.1.3 Environmental Coupling vs. Classical Noise . .6 1.1.4 Simple Model - Dephasing . 10 1.1.5 Experimental Simulation . 10 1.2 Simulation Proposals . 13 1.2.1 Our Proposal . 14 1.3 Thesis Contents and Structure . 17 1.3.1 Thesis Structure . 17 2 General Theory 20 2.1 Quantum Mechanics Review . 20 2.1.1 Mixed States . 21 2.2 Rotating Wave Approximation . 22 2.3 Bloch Sphere Representation . 24 2.3.1 Three-level Bloch Sphere . 26 2.4 Rubidium 87 Structure . 27 2.4.1 Fine and Hyperfine Structure . 27 Polarisation Selection Rules . 29 2.4.2 Rubidium 87 3-Level System . 29 3 Cold Atoms Cloud Creation 32 3.1 Optical System . 34 Master Laser . 35 Repumper Laser . 36 Slave Laser . 37 3.2 Vacuum System and Magnetic Gradient Coils . 40 Cooling Beams . 40 3.3 Experimental Control . 42 3.4 Experimental Procedure . 43 Absorption Imaging . 44 3.4.1 Select System Measurements . 44 Master Lock Calibration . 45 Loading Rate . 46 Temperature Measurements . 47 3.5 Concluding Remarks . 49 4 State Readout - Stern-Gerlach Separation 50 4.1 Stern-Gerlach Theory . 51 4.2 Creating Magnetic Field Gradients . 52 4.2.1 Finite Coil Time Constant . 53 4.2.2 Coil Switch Off and Eddy Currents . 54 Magnetic Energy Dissipation . 55 Eddy Currents . 56 4.2.3 Non-Linear Zeeman Shifts . 57 4.3 Experimental Implementation . 60 4.3.1 Image Processing . 65 4.3.2 Separation Quantitative Analysis . 66 Quadratic Zeeman Shift Results . 71 4.4 Concluding Remarks . 71 5 State Preparation - Optical Pumping 74 5.1 Optical Pumping Overview . 75 5.1.1 Optical Pumping Recovery Beam . 76 5.2 Rubidium 87 F = 2 Optical Pumping . 78 5.2.1 Experimental Results . 79 5.3 Rubidium 87 F = 1 Optical Pumping . 82 5.3.1 Experimental Results . 85 Quarter Waveplate Angle . 85 Pumping Beam Intensity . 88 5.4 Concluding Remarks . 88 6 Nearest Neighbour Coupling - Magnetic Dipole Transitions 90 6.1 Bias Field Creation . 91 6.2 Oscillating Magnetic Field Creation . 94 6.3 Finding the Resonance with Adiabatic Transitions . 98 6.3.1 Landau-Zener Theory . 99 6.3.2 Adiabatic Transition Results . 100 6.4 Rabi Oscillations . 103 6.4.1 Rabi Oscillation Results . 108 Resonant Rabi Frequency . 112 6.5 Ramsey Fringes . 113 6.5.1 Ramsey Sequence . 115 Results . 117 6.6 Concluding Remarks . 120 7 Hamiltonian Diagonal Time Dependence 121 7.1 Experimental Implementation . 122 7.2 Pure Tone Perturbation . 123 7.3 Random Broadband Spectrum . 133 7.3.1 Spectral Shaping . 136 7.3.2 Computer Simulations . 138 7.3.3 Experimental Results . 143 7.4 Concluding Remarks . 152 8 Next Steps 153 8.1 Breaking the Symmetry . 153 8.1.1 Higher Order Magnetic Shift . ..
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