Quantum thermodynamics of integrable and near-integrable atomic systems

TL;DR

This thesis investigates quantum thermodynamics in 1D Bose gases, focusing on quantum Otto cycles, deriving new relations for entropy, benchmarking GHD, and simulating quantum engines with SPGPE, highlighting experimental relevance and theoretical advancements.

Contribution

It introduces a new Maxwell relation for entropy, benchmarks GHD for quantum thermodynamics, and demonstrates quantum Otto cycle simulations using SPGPE in 1D Bose gases.

Findings

Performance of quantum Otto cycle expressed via atom correlations

Derived Maxwell relation links entropy to measurable correlations

Simulated quantum engine cycle with SPGPE in 1D Bose gases

Abstract

In this thesis, we explore various aspects of equilibrium and nonequilibrium thermodynamics for ultracold atomic gases, with a focus on the experimentally realisable one-dimensional (1D) Bose gas. This is a paradigmatic example of an interacting many-body system, which is integrable in the uniform limit and near-integrable otherwise. We first investigate a quantum thermodynamic Otto cycle driven by a quench of interaction strength of a 1D Bose gas. For the case of a sudden quench in a uniform 1D Bose gas, we demonstrate how the performance of this highly nonequilibrium quantum thermal machine may be expressed in terms of atom-atom correlations. Further, we derive a new Maxwell relation which allows one to express entropy, which is generally difficult to ascertain in quantum systems, in terms of Glauber's local second-order correlation function, which are experimentally measurable. We next perform benchmarks of GHD in order to ascertain the regimes where such a theory may be applied, and then utilize it to investigate the interaction strength-driven quantum Otto cycle in a harmonically trapped 1D Bose gas. However, to realise such an engine in an experimentally realistic manner would require modelling thermalisation with external reservoirs, which is currently beyond the scope of GHD. Yet, the classical $c$-field stochastic-projected Gross-Pitaevskii equation (SPGPE) method is capable of simulating tunnel-coupling pairs of 1D Bose gases in the weakly interacting regime. We therefore utilise this numerical method to simulate the \emph{full} quantum Otto engine cycle, realised through a single working fluid tunnel-coupled to two 1D Bose gases, which constitute the external (hot and cold) reservoirs.