Engineered Reservoirs for Thermalization of Many-Body Quantum Systems

Lincoln D. Carr, Daniel Jaschke, Inés de Vega

Karamoko Soumahoro, Alison Valbuena, Roman Senkov

Vijit V. Nautiyal

We theoretically investigate the finite-time performance of a quantum thermochemical engine utilizing a harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate regime as the working fluid. The proposed engine operates in an Otto cycle, where the unitary work strokes are simulated through a quench of the interatomic interactions of the 1D Bose gas. In the work strokes, the working fluid is treated as a closed quantum many-body system that undergoes dynamic evolution, beginning from an initial thermal equilibrium state at a nonzero temperature. On the other hand, during the thermalization strokes, the working fluid is treated as an open many-body quantum system in diffusive contact with a thermal reservoir, allowing particle exchange alongside the transfer of heat. Using a c-field approach, we demonstrate that the engine's operation is enabled by the chemical work done on the working fluid through the flow of particles from the hot reservoir. We examine the finite-time performance of the proposed quantum thermochemical engine in two extreme regimes: (i) the out-of-equilibrium regime (sudden quench), which yields near-maximum power (due to fast driving of the system) while compromising efficiency, and (ii) the quasistatic (near-adiabatic) limit, which approaches maximum efficiency but generates zero power output due to slow driving of the system. Notably, we show that using chemical work allows the engine to achieve efficiencies close to the near-maximum (quasistatic) limit, even in the out-of-equilibrium regime, while maintaining high power output. Thus, in the out-of-equilibrium operational regime, our proposed engine provides a favorable trade-off between efficiency and power output. We also draw connections to previous research, particularly the case of an adiabatic engine cycle operating at zero temperature. We show that this zero-temperature scenario establishes an upper bound on the efficiency and work of our proposed thermochemical engine operating at nonzero temperatures.

Felix M. Izrailev

Vijit V. Nautiyal

The development of the theory of thermodynamics dates back nearly two centuries, to when the need arose to comprehend and enhance the performance of a novel technology of that era, the heat engine. Extending the classical concepts related to the properties of heat and work into the quantum realm forms the foundation of an emerging field of research known as quantum thermodynamics. To unify the disparate theories of classical thermodynamics and quantum mechanics, a thoroughly developed theoretical framework is necessary. Quantum heat engines provide a fundamental platform for this purpose. Many-body quantum heat engines, in particular, can provide important insights into the potential utilisation of exotic quantum phenomena, such as entanglement and quantum coherence, for building quantum devices that can surpass their classical counterparts in performance. One-dimensional (1D) Bose gases are a paradigmatic example of an interacting quantum many-body system that can be used as a versatile platform for building heat engines to test the thermodynamic theories in the quantum regime. The versatility of this platform comes through the routine experimental realisability of 1D Bose gases, with precise control of their internal and external properties, such as the strength of inter-atomic interactions and external confinement, and the presence of quantum many-body effects. In recent years, there has been an increased focus on exploiting the unique properties of ultracold atomic gases to realize many-body quantum heat engines. Despite this heightened attention and the resulting significant advances at the level of theoretical proposals, experimental feasibility and practical utilization of such engines remains at its infancy. Achieving significant advances at the experimental level requires a deeper understanding of the fundamental components of quantum-gas heat engines. Motivated by this goal, in this thesis we propose a novel and experimentally realistic quantum many-body heat engine that operates in an Otto cycle and uses a weakly interacting harmonically trapped 1D Bose gas as a working fluid. To execute work during the work strokes, we use a quench of the strength of interparticle interactions; when the quench is sudden with respect to the longitudinal dynamics, it maximises the power output. The interaction-induced work strokes are implemented by treating the working fluid as an isolated quantum many-body system undergoing a dynamical evolution starting from a finite temperature thermal equilibrium state. Furthermore, to optimize the performance of this interaction-driven quantum Otto cycle in an experimental scenario, we undertake a comprehensive numerical investigation of the dynamics of the system-reservoir coupling during the heat transfer strokes. We model the heat transfer strokes by treating the working substance as an open quantum many-body system that is coupled to a reservoir.After providing an overview of recent advances in the field of quantum thermodynamics and the background theory of 1D Bose gases in Chapters 1 and 2 we present the main results of this thesis in Chapters 3, 4 and 5. In Chapter 3, we study the individual interaction-induced work strokes of the Otto cycle with a weakly interacting 1D Bose gas as the working fluid. We evaluate the instantaneity of the sudden quench, specifically, identifying the minimum timescales required to perform the sudden quench of the interaction strength without invoking the transverse dynamics. Knowledge of these timescales enables us to perform the sudden quench in an experimental setting while ensuring that the system retains its 1D characteristics and the theory of 1D Bose gas is applicable. Additionally, we determine the time scales governing the opposite scenario of near-adiabatic quench which corresponds to minimum irreversible work in the engine cycle and hence maximum efficiency. This will help us benchmark the sudden quench engine's performance compared to a nearly ideal (near-adiabatic) scenario corresponding to maximum efficiency.Next, in Chapter 4, we analyze the heat transfer strokes of the Otto cycle, where the system is coupled to a reservoir. Using the c-field approach, we simulate the coupling dynamics of the system with both finite and infinite-size reservoirs. During the heat transfer stroke of the quantum Otto cycle, we treat the working fluid as an open quantum many-body system that is in thermal and diffusive contact with another quantum many-body system serving as the reservoir. In our real-time dynamical simulations of the engine strokes, we use a c-field approach based on the stochastic projected Gross-Pitaevskii equation. This approach enables us to treat both the working fluid and the hot and cold reservoirs as independent quantum many-body systems with chemical potential and temperature imbalances. To model the heat transfer strokes of such an engine with a finite-size reservoir, we use a tunnel-coupled model of two quasicondensates that treats both the system and the reservoir microscopically. Our analysis incorporates the impact of both finite-time operation and finite-size reservoirs in the engine cycle to gain a deeper understanding of the operational feasibility of such engines. Our results indicate that, in contrast to the common assumption of near-instantaneous heat transfer between the system and the reservoir, the thermalisation time of the system during these heat transfer strokes is non-negligible when compared to the duration of work strokes even in the near-adiabatic quench. This observation holds true even in the case of coupling the system with an infinite reservoir during the heat transfer strokes. Moreover, we demonstrate that for a finite-size reservoir, the initial dynamics (namely fast initial energy transfer) in the tunnel-coupled model of two quasicondensates can be leveraged to reduce the total driving time and hence increase the power output of the engine. Finally, in Chapter 5, we explore an alternate protocol that involves performing chemical work on the system during the heat transfer strokes to boost the efficiency and power output of the quantum Otto engines with a 1D Bose gas as a working fluid. We compare the performance of the sudden quench engine with an engine driven by a near-adiabatic and a finite-time quench of the interaction strength with respect to the longitudinal dynamics. We then conclude the thesis by summarising our main findings and presenting open questions for future work in the final chapter, Chapter 6.

Taira Kawamura, Ryo Hanai, Yoji Ohashi

We theoretically propose an idea based on reservoir engineering to process the structure of a Fermi edge to split into multiple Fermi edges, so as to be suitable for the state which we want to realize. When one appropriately tunes the chemical-potential difference between two reservoirs being coupled with the system, the system is shown to be in the non-equilibrium steady state with the momentum distribution having a two-edge structure. We argue that these edges play similar roles to two Fermi surfaces, which can be designed to realize exotic quantum many-body states. To demonstrate this, we consider a model driven-dissipative two-component Fermi gas with an attractive interaction as a paradigmatic example and show that it exhibits an unconventional Fermi superfluid. While the superfluid order parameter of this state has the same form as that in the Fulde-Ferrell state discussed in metallic superconductivity under an external magnetic field, the former non-equilibrium pairing state is not accompanied by any spin imbalance. Our proposed reservoir engineering to process the Fermi momentum distribution would provide further possibilities of many-body quantum phenomena beyond the thermal equilibrium case.