Non-equilibrium Dynamics of Tunnel-Coupled Superfluids: Relaxation to a Phase-Locked Equilibrium State in a One-Dimensional Bosonic Josephson Junction (Springer Theses)

The relaxation of isolated quantum many-body systems is a major unsolved problem of modern physics, which is connected to many fundamental questions. However, realizations of quantum many-body systems which are both well isolated from their environment and accessible to experimental study are scarce. In recent years, the field has experienced rapid progress, partly attributed to ultra-cold atoms. This book presents the experimental study of a relaxation phenomenon occurring in a one-dimensional bosonic Josephson junction. The system consists of two 1D quasi Bose-Einstein condensates of 87 Rb, magnetically trapped on an atom chip. Using radio-frequency dressing, the author deforms a single harmonic trap, in which the atoms are initially condensed, into a double-well potential and realizes a splitting of the wave function. A large spatial separation and a tilt of the double-well enable the preparation of a broad variety of initial states by precisely adjusting the initial population and relative phase of the two wave packets, while preserving the phase coherence. By re-coupling the two wave packets, the author investigates tunneling regimes such as Josephson (plasma) oscillations and macroscopic quantum self-trapping. In both regimes, the tunneling dynamics exhibits a relaxation to a phase-locked equilibrium state contradicting theoretical predictions. The experimental results are supported with an empirical model that allows quantitative discussions according to various experimental parameters. These results illustrate how strongly the non-equilibrium dynamics differ from the equilibrium one, which is well described by thermodynamics and statistical physics. Supervisor’s Foreword 6 Abstract 8 Preface 10 References 12 List of Publications Related to this ThesisParts of this thesis have been published in:Relaxation to a Phase-locked Equilibrium State in a One-dimensional Bosonic Josephson JunctionM. Pigneur, T. Berrada, M. Bonneau, T. Schumm, E. Demler, J. Schmiedmayer, Physical Review Letters 120, 173601, published April 27, 2018Analytical Pendulum Model for a Bosonic Josephson JunctionM. Pigneur and J. Schmiedmayer, Physical Review A 98, 063632, published December 26, 2018These results were reported in the following newspaper and scientific popularization journal:Ultrakalte Atomwolken verblüffen PhysikerDer Standard, 12 May 2018Quantenzigarren in rätselhaftem gleichtaktM. Pigneur, Spektrum der Wissenschaft 9.18, Rubrik Forschung aktuell, September, 2018 15 Acknowledgements 16 Contents 17 1 Theoretical Framework 19 1.1 The Ideal Bose Gas 19 1.1.1 Bose Statistics and Density of States 19 1.1.2 Bose-Einstein Condensation in 3D 20 1.1.3 Quasi-condensation in 1D 23 1.2 Weakly Interacting Bose Gas 24 1.2.1 Many-Body Hamiltonian in Second Quantization 24 1.2.2 Mean-Field Model: The Gross-Pitaevskii Equation 26 1.2.3 The Thomas-Fermi Limit 27 1.2.4 Crossover 3D/1D 29 1.3 Bose Gases in a Double-Well Potential 33 1.3.1 Two-Mode Approximation 33 1.3.2 Ideal Dynamics in the Mean-Field Formalism 35 1.3.3 Two-Mode Bose-Hubbard Model in the Quantum Formalism 51 1.3.4 Dynamics with Fluctuations in the Semi-classical Picture 55 1.4 Conclusion of the Theoretical Chapter 76 References 76 2 Experimental Setup and Measurement of the Observables 79 2.1 Overview of the Experimental Sequence 79 2.2 Experimental Apparatus 81 2.2.1 Vacuum Chamber and Rubidium Dispensers 81 2.2.2 Copper Structure and Atom Chip 82 2.2.3 External Coils 84 2.2.4 Lasers System and Optics 84 2.2.5 Radio-Frequency Generators 86 2.2.6 Computer Control and Acquisition 87 2.3 Magnetic Trapping of Atoms with an Atom Chip 87 2.3.1 Magnetic Trapping with Static Fields 87 2.3.2 Magnetic Trapping with Radio Frequency Fields 95 2.4 Imaging Systems and Data Analysis 109 2.4.1 Imaging Systems 109 2.4.2 Estimation of the Relative Phase 120 2.4.3 Estimation of the Atom Number Difference 129 References 132 3 Relaxation of the Josephson Oscillations in a 1D-BJJ 134 3.1 Preparation of the Initial State 134 3.1.1 Experimental Requirements 134 3.1.2 Coherent Splitting of the Wave Function by Linear Ramp 137 3.1.3 Phase Accumulation 139 3.1.4 Recoupling 142 3.2 Relaxation of the Oscillating Tunneling Dynamics 145 3.2.1 Relaxation Versus Dephasing and Dissipation 145 3.2.2 Empirical Model for the Relaxation 151 3.2.3 Experimental Dependence of the Relaxation Timescale 160 3.3 Conclusion 174 References 175 4 Transition to a Relaxation-Free Regime 176 4.1 Initial State Preparation by Asymmetric Splitting 176 4.2 Decay and Relaxation 179 4.2.1 Experimental Evolution of the Mean Values 179 4.2.2 Dissipative BJJ in the MQST 180 4.2.3 Relaxation Through Local Dynamics 184 4.3 Transition to a Relaxation-Free Regime 190 4.4 Conclusion 193 References 193 5 Relaxation During the Splitting of a 1D Bose Gas 194 5.1 Adiabatic Splitting 195 5.1.1 Estimation of the Effective Duration of the Relaxation 195 5.1.2 Simulation of a Linear Splitting with Relaxation 196 5.2 Two-Step Splitting 198 5.2.1 Two-Step Splitting with Relaxation 198 5.2.2 Preliminary Results on the Implementation of the First Ramp 198 References 204 Front Matter ....Pages i-xx Theoretical Framework (Marine Pigneur)....Pages 1-60 Experimental Setup and Measurement of the Observables (Marine Pigneur)....Pages 61-115 Relaxation of the Josephson Oscillations in a 1D-BJJ (Marine Pigneur)....Pages 117-158 Transition to a Relaxation-Free Regime (Marine Pigneur)....Pages 159-176 Relaxation During the Splitting of a 1D Bose Gas (Marine Pigneur)....Pages 177-187