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Physical review. E

Performance enhancement of quantum Brayton engine via Bose-Einstein condensation

Huilin Ruan, Jiehong Yuan, Yang Xu, Jizhou He, Yongli Ma, Jianhui Wang

Published Feb 23, 2024• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.109.024126

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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 consider a quantum Brayton refrigeration cycle consisting of two isobaric and two adiabatic processes, using an ideal Bose gas of finite particles confined in a harmonic trap as its working substance. Quite generally, such a machine falls into three different cases, classified as the condensed region, non-condensed phase, and regime across the critical point. When the refrigerator works near the critical region, both figure of merit and cooling load are significantly improved due to the singular behavior of the specific heat, and the coefficient of performance at maximum figure of merit is much larger than the Curzon–Ahlborn value. With the machine in the non-condensed regime, the coefficient of performance for maximum figure of merit agrees well with the Curzon–Ahlborn value.
At low-temperatures a gas of bosons will undergo a phase transition into a quantum state of matter known as a Bose-Einstein condensate (BEC), in which a large fraction of the particles will occupy the ground state simultaneously. Here we explore the performance of an endoreversible Otto cycle operating with a harmonically confined Bose gas as the working medium. We analyze the engine operation in three regimes, with the working medium in the BEC phase, in the gas phase, and driven across the BEC transition during each cycle. We find that the unique properties of the BEC phase allow for enhanced engine performance, including increased power output and higher efficiency at maximum power.
Abstract At low-temperatures a gas of bosons will undergo a phase transition into a quantum state of matter known as a Bose–Einstein condensate (BEC), in which a large fraction of the particles will occupy the ground state simultaneously. Here we explore the performance of an endoreversible Otto cycle operating with a harmonically confined Bose gas as the working medium. We analyze the engine operation in three regimes, with the working medium in the BEC phase, in the gas phase, and driven across the BEC transition during each cycle. We find that the unique properties of the BEC phase allow for enhanced engine performance, including increased power output and higher efficiency at maximum power.
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.
Abstract This research investigates the endoreversible quantum Stirling engine using the Bose-Einstein Condensate (BEC) as a working medium trapped in a generic law potential. The engine operates endoreversibly in order to capture a realistic condition, where the temperature of the working medium depends on the heating and cooling stroke times. The Fourier conduction law is applied to govern the rate of heat transfer between the system and the thermal reservoir in finite time, whilst in isoenergetic strokes, an infinite time is required to accomplish the thermal equilibrium. The results show that the condensed phase of BEC has the ability to enhance the efficiency of the engine, especially at temperatures near absolute zero. In conclusion, adjusting the temperature and volume ratio can optimize performance to achieve higher efficiency and power output of the Stirling engine.
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.