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arXiv:1803.03734

Quantum heat engine based on trapped Bose gases: Its maximum efficiency can approach the Carnot value at finite power

Wang, Jianhui, Jizhou He, Yongli Ma

Published Mar 10, 2018• 1 citation
arXivHTMLPDF

Abstract

It was reported that, if and only if the specific heat, correlation length, and dynamical exponents $α, ν$ and $z$, fulfill the condition $α-zν>0$, the phase transitions can enable a quantum heat engine to approach Carnot efficiency at finite power. We start our analysis via a different approach in which the effects of interaction and fluctuations on the Hamiltonian of a trapped dilute Bose gas belonging to the same universality as $XY$ model. Based on models of quantum Otto heat engines, we find the general expression of the efficiency which includes the correction due to interaction and fluctuations at the critical point, and show that, near the Bose-Einstein-condensation point with $α-zν<0$, energy fluctuations could enable attaintment of the Carnot efficiency with nonvanishing power. Such quantum heat engines can also be realized by changing the shape of the trap confining the ideal and weakly interacting Bose gas during the adiabatic processes of the cycle. These quantum heat engines working with the trapped Bose gases, which are based on techniques of cooling Bose condensates and could be realizable at present technology.

DOI
10.48550/arxiv.1803.03734

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It was reported that, if and only if the specific heat, correlation length, and dynamical exponents α,να, να,ν and zzz, fulfill the condition α−zν>0α-zν>0α−zν>0, the phase transitions can enable a quantum heat engine to approach Carnot efficiency at finite power. We start our analysis via a different approach in which the effects of interaction and fluctuations on the Hamiltonian of a trapped dilute Bose gas belonging to the same universality as XYXYXY model. Based on models of quantum Otto heat engines, we find the general expression of the efficiency which includes the correction due to interaction and fluctuations at the critical point, and show that, near the Bose-Einstein-condensation point with α−zν<0α-zν<0α−zν<0, energy fluctuations could enable attaintment of the Carnot efficiency with nonvanishing power. Such quantum heat engines can also be realized by changing the shape of the trap confining the ideal and weakly interacting Bose gas during the adiabatic processes of the cycle. These quantum heat engines working with the trapped Bose gases, which are based on techniques of cooling Bose condensates and could be realizable at present technology.
Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a d-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in N-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.
We investigate quantum Otto engines operating with a weakly interacting Bose gas confined in a cubic box with periodic boundary conditions. Our study focuses on two approaches to realizing adiabatic processes: varying the system volume and adjusting the interaction strength. We analyze the impact of Bose-Einstein condensation and interparticle interaction effects on engine performance, particularly power output and efficiency. Additionally, we explore the advantages of operating near the critical point of condensation, where quantum phenomena may enhance engine performance. Our findings underscore the significance of phase transitions and many-body effects in improving machine performance.
Heat engines constitute the major building blocks of modern technologies. However, conventional heat engines with higher power yield lesser efficiency and vice versa and respect various power-efficiency trade-off relations. This is also assumed to be true for the engines operating in the quantum regime. Here we show that these relations are not fundamental. We introduce quantum heat engines that deliver maximum power with Carnot efficiency in the one-shot finite-size regime. These engines are composed of working systems with a finite number of quantum particles and are restricted to one-shot measurements. The engines operate in a one-step cycle by letting the working system simultaneously interact with hot and cold baths via semilocal thermal operations. By allowing quantum entanglement between its constituents and, thereby, a coherent transfer of heat from hot to cold baths, the engine implements the fastest possible reversible state transformation in each cycle, resulting in maximum power and Carnot efficiency. Finally, we propose a physically realizable engine using quantum optical systems.
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.
We investigate the finite-power performance of quantum heat engines working in the linear response regime where the temperature gradient is small. The engine cycles with working substances of ideal harmonic systems consist of two heat transfer and two adiabatic processes, such as the Carnot cycle, Otto cycle, and Brayton cycle. By analyzing the optimal protocol under maximum power we derive the explicitly analytic expression for the irreversible entropy production, which becomes the low dissipation form in the long duration limit. Assuming the engine to be endoreversible, we derive the universal expression for the efficiency at maximum power, which agrees well with that obtained from the phenomenological heat transfer laws holding in the classical thermodynamics. Through appropriate identification of the thermodynamic fluxes and forces that a linear relation connects, we find that the quantum engines under consideration are tightly coupled, and the universality of efficiency at maximum power is confirmed at the linear order in the temperature gradient.
We consider the finite-time operation of a quantum heat engine whose working substance is composed of a two-level atomic system. The engine cycle, consisting of two quantum adiabatic and two quantum isochoric (constant-frequency) processes and working between two heat reservoirs at temperatures Th{T}_{h}Th​ and Tc{T}_{c}Tc​(<(<(<Th){T}_{h})Th​), is a quantum version of the classical Otto cycle. By optimizing the power output with respect to two frequencies, we obtain the efficiency at maximum power output (EMP) and analyze numerically the effects of the times taken for two adiabatic and two isochoric processes on the EMP. In the absence of internally dissipative friction, we find that the EMP is bounded from the upper side by a function of the Carnot efficiency ${\ensuremath{\eta}}_{C}$, ${\ensuremath{\eta}}_{+}={\ensuremath{\eta}}_{C}^{2}/[{\ensuremath{\eta}}_{C}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C})\mathrm{ln}(1\ensuremath{-}{\ensuremath{\eta}}_{C})]$, with ${\ensuremath{\eta}}_{C}=1\ensuremath{-}{T}_{c}/{T}_{h}$. This analytic expression is confirmed by our exact numerical result and is identical to the one derived in an engine model based on a mesoscopic or macroscopic system. If the internal friction is included, we find that the EMP decreases as the friction coefficient increases.