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Advances in Laser Slowing, Cooling, and Trapping Using Narrow Linewidth Optical Transitions

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Advances in Laser Slowing, Cooling, and Trapping Using Narrow Linewidth Optical Transitions Advances in Laser Slowing, Cooling, and Trapping using Narrow Linewidth Optical Transitions by John Patrick Bartolotta B.S., University of Connecticut, 2014 M.S., University of Connecticut, 2016 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Physics 2021 ii Bartolotta, John Patrick (Ph.D., Physics) Advances in Laser Slowing, Cooling, and Trapping using Narrow Linewidth Optical Transitions Thesis directed by Prof. Murray J. Holland Laser light in combination with electromagnetic traps has been used ubiquitously throughout the last three decades to control atoms and molecules at the quantum level. Many approaches with varying degrees of reliance on dissipative processes have been discovered, investigated, and implemented in both academic and industrial settings. In this thesis, we theoretically investigate and propose three practical techniques which have the capacity to slow, cool, and trap particles with narrow linewidth optical transitions. Each of these methods emphasizes a high degree of coherent control over quantum states, which lends their operation a reduced reliance on spontaneous emission and thus makes them appealing candidates for application to systems that lack closed cycling transitions. In a more general setting, we also study the transfer of entropy from a quantum system to a classically-behaved coherent light field, and therefore advance our understanding of the role of dissipative processes in optical pumping and laser cooling. First, we describe theoretically a cooling technique named \sawtooth wave adiabatic passage cooling," or \SWAP cooling," which was discovered experimentally at JILA and has since been implemented elsewhere with various atomic species. Second, we discuss some of the results of an experimental realization of SWAP cooling and connect them to the theoretical model. Third, we propose the extension of the coherent mechanism underlying SWAP cooling to the additional task of trapping in a configuration named the \SWAP magneto-optical trap," or \SWAP MOT." Fourth, we propose a method to fundamentally speed up the adiabatic transfer process required for these techniques by using a shortcut-to-adiabaticity protocol based on Lewis-Riesenfeld invariants. Lastly, we propose and theoretically analyze a simple Gedankenexperiment which can be used to study the potential transfer of entropy from an ensemble of particles to a coherent light source. Dedication To my fianc´eeKelsey, who knows me more than I know myself. To my parents, Robert and Karen. Thanks for always believing in me. To my siblings, Mary and Sarah. I wouldn't be who I am today without you. To the friends and family who helped to shape me along the way. iv Acknowledgements There has never been a time when I recognized the importance and impact of others on my work more than the years I spent as a graduate student at CU Boulder. My challenging journey toward doctorship would certainly not have been possible without the support, reassurance, and wisdom of my mentors and colleagues. I would first like to thank Murray for granting me the opportunity to grow as a person and physicist under his advisement. I always felt supported by him in both my studies and ex- tracurricular activities. Thanks to Jinx for teaching me the importance of physical intuition over mathematical formalism. Thanks to Athreya Shankar, Simon J¨ager,Jarrod Reilly, Haonan Liu, Liang-Ying Chih, and Victor Colussi for being supportive group mates. Thanks to Graeme Smith, John Bohn, Dana Anderson, Jun Ye, James Thompson, Ana Maria Rey, Shiqian Ding, Yewei Wu, Matthew Norcia, and Julia Cline for countless stimulating and productive discussions. I am indebted to many people and organizations for balancing my lifestyle with activities separate from my academic pursuits. Thanks to the many local climbing gyms and outdoor crags for challenging me both physically and mentally with fantastic climbing routes. Thanks to William Lewis and Ben Galloway for memorable game nights and career advice. Thanks to the members of CU-Prime for working toward an inclusive and equitable physics community. And many thanks to the staff at JILA and the CU Physics Department. I would not have continued to pursue a physics career without the mentorship of several motivating physicists at the University of Connecticut. Many thanks to Vasili Kharchenko, Richard T. Jones, and Philip Mannheim for these experiences. v Contents Chapter 1 Context and outline 1 2 Introduction 3 2.1 Coherent models of light-matter interaction . 3 2.1.1 First quantization: quantum treatment of matter . 5 2.1.2 The two-level particle . 8 2.1.3 Interaction of a moving two-level quantum system with a classical light field . 10 2.1.4 Second quantization: interaction of motionless two-level quantum system with a quantized light field in a cavity . 12 2.1.5 The spontaneous emission process . 14 2.2 Theory of open quantum systems . 16 2.2.1 The density matrix formalism . 17 2.2.2 The quantum master equation . 19 2.2.3 The Lindblad superoperator in laser slowing, cooling, and trapping . 21 2.2.4 The Monte Carlo wave function method . 23 2.3 Doppler-based cooling and trapping processes . 25 2.3.1 Approximation of classical particle motion . 25 2.3.2 Cooling force . 27 2.3.3 Minimum temperature . 29 2.3.4 The magneto-optical trap . 31 vi 3 SWAP cooling: theoretical investigation 35 3.1 Introduction . 35 3.2 Basic mechanism . 37 3.3 System dynamics . 40 3.4 Dynamics in the high-velocity regime . 41 3.4.1 Resonance times and intervals in the adiabatic limit . 42 3.4.2 Dressed state picture . 43 3.4.3 Coherent dynamics . 45 3.4.4 High-velocity regime dynamics including dissipation . 46 3.5 Forces and capture range . 47 3.5.1 Conservative forces . 47 3.5.2 Forces including dissipation . 50 3.6 Effect of higher-order processes . 52 3.6.1 Doppleron resonances . 52 3.6.2 Bragg oscillations . 54 3.7 Temperature limit as γ 0................................ 55 ! 3.8 Cooling efficiency . 59 3.9 Conclusion . 59 4 SWAP cooling: experimental results and comparison to theory 62 4.1 Introduction . 63 4.2 Basic mechanism . 64 4.3 Numerical demonstration of basic mechanism . 65 4.4 Demonstration of steady-state cooling and phase space compression . 66 4.5 Comments on entropy removal . 68 4.6 Cooling forces . 69 4.7 Temperature measurement and comparison to simulation . 71 vii 4.8 Conclusion . 74 5 SWAP MOT 75 5.1 Introduction . 75 5.2 SWAP MOT mechanism . 77 5.3 Model and semiclassical approximations . 81 5.4 Variant of quantum trajectories . 85 5.5 Validity of three-state basis in SWAP MOT simulation . 88 5.6 Phase space dynamics . 90 5.6.1 Choosing appropriate experimental parameters . 91 5.6.2 Cooling and trapping of the molecule YO . 94 5.6.3 Characteristic dynamics in different phase space regions . 96 5.6.4 Phase space compression . 99 5.6.5 MOT loading . 100 5.7 Equilibrium temperatures and cloud sizes . 102 5.7.1 SWAP MOT effective potential . 105 5.8 Conclusion . 106 6 Speeding up particle slowing using shortcuts to adiabaticity 108 6.1 Introduction . 109 6.2 Motivation for the speed-up protocol . 111 6.3 Lewis-Riesenfeld Invariant-based inverse engineering . 113 6.4 Model . 114 6.4.1 System dynamics . 116 6.4.2 Eigensystem in a momentum subspace . 118 6.4.3 Deriving detuning profiles from the auxiliary equations . 119 6.4.4 Bloch sphere trajectories . 122 6.5 Slowing dynamics in classical phase space . 124 viii 6.6 Slowing Examples . 127 6.7 Robustness . 132 6.8 Conclusion and Outlook . 136 7 Entropy transfer from a quantum particle to a classical coherent light field 139 7.1 Introduction . 140 7.2 Motivation . 141 7.3 Model . 142 7.4 Calculating the final cavity field state . 143 7.5 Q-function for the final cavity field state . 146 7.6 Calculating the fidelity between the initial and final cavity field states . 148 7.6.1 Fidelity in the thermodynamic limit . 148 7.7 Analyzing the fidelity result . 150 7.8 Bayesian analysis . 152 7.9 Calculating entropies and mutual information . 154 7.9.1 Mutual information from cavity measurements . 156 7.9.2 Quantum mutual information . 156 7.10 Analyzing the entropies and mutual information . 159 7.10.1 Entropy of the spontaneous photon . 162 7.11 Additional calculations . 163 7.11.1 Displaced final cavity field photon distribution . 163 7.11.2 Fidelity in the infinite coupling limit m 0 . 167 ! 7.12 Conclusion . ..
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