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arXiv:2012.10241 · New Journal of Physics

Quantum Otto refrigerators in finite-time cycle period

Guangqian Jiao, Yang Xiao, Jizhou He, Yongli Ma, Jianhui Wang

Published Jun 1, 2021• 20 citations
arXivHTMLPDF

Abstract

Abstract Finite-time cycle period for a quantum Otto machine implies that either an adiabatic stroke or an isochoric process proceeds in finite time duration. The quantum Otto refrigerators under consideration consist of two adiabatic strokes, where the system (isolated from the heat reservoir) undergoes finite-time unitary transformation, and two isochoric steps, where the system may not reach thermal equilibrium even at the respective ends of the two stages due to finite-time interaction intervals. Using two-time projective measurement method, we find the probability distribution functions of both coefficient of performance and cooling load, which are dependent on the time duration along each process. With these distributions we find the analytical expressions for the performance parameters as well as their fluctuations. We then numerically determine the performance and fluctuations for the refrigerator operating with a two-level system employed in a recent experimental implementation. Our results clarify the role of finite-time durations of four processes on the performance and fluctuations of the quantum Otto refrigerators.

DOI
10.1088/1367-2630/ac08e4

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Abstract Finite-time cycle period for a quantum Otto machine implies that either an adiabatic stroke or an isochoric process proceeds in finite time duration. The quantum Otto refrigerators under consideration consist of two adiabatic strokes, where the system (isolated from the heat reservoir) undergoes finite-time unitary transformation, and two isochoric steps, where the system may not reach thermal equilibrium even at the respective ends of the two stages due to finite-time interaction intervals. Using two-time projective measurement method, we find the probability distribution functions of both coefficient of performance and cooling load, which are dependent on the time duration along each process. With these distributions we find the analytical expressions for the performance parameters as well as their fluctuations. We then numerically determine the performance and fluctuations for the refrigerator operating with a two-level system employed in a recent experimental implementation. Our results clarify the role of finite-time durations of four processes on the performance and fluctuations of the quantum Otto refrigerators.
We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cycle, which are dependent on the time duration along each process. With these, we derive the analytical expressions for the thermodynamic quantities of the two-level heat engine, such as total work, thermodynamic efficiency, entropy production, and work fluctuations, in which effects of coherence, squeezing, inner friction and finite-time heat exchange are included. We then numerically determine the thermodynamic quantities and the fluctuations using the parameters employed in the experimental implementation. Our results clarify the role of coherence and squeezing in the performance and fluctuations in the quantum Otto engines.
We derive the general probability distribution function of stochastic work for quantum Otto engines in which both the isochoric and driving processes are irreversible due to finite time duration. The time-dependent work fluctuations, average work, and thermodynamic efficiency are explicitly obtained for a complete cycle operating with an analytically solvable two-level system. The effects of the irreversibility originating from finite-time cycle operation on the thermodynamic efficiency, work fluctuations, and relative power fluctuations are discussed.
Devising and constructing quantum many-body heat engines is a key challenge of quantum thermodynamics. Most of the research in this field assumes the strokes to be ideal transformations. Here, the authors study the performance of realistic Otto engines with finite-time duration, whose working substance is made of free-fermion systems. They provide analytic expressions for the work and the power delivered through imperfect adiabatic and isochoric strokes. These findings are applied to the case study of an Ising-like quantum Otto cycle.
Experimental demonstration of a truly quantum mechanical solid-state heat engine or refrigerator remains elusive up to now. Here, a four-stroke quantum refrigerator that can be realized using a superconducting qubit coupled alternately to two resonators with embedded reservoirs is analyzed theoretically. Besides being a practically feasible thermal machine, this concept presents a number of fundamentally interesting features. At high frequencies, the system exhibits nearly coherent dynamics, leading to quantum oscillations in cooling power versus operation frequency. At intermediate frequencies, an ideal Otto cycle can be realized. In the nearly adiabatic regime, the cooling power is quadratic in frequency and can be separated to classical and quantum contributions. Interestingly, it is shown here that quantum coherence leads always to performance that is inferior as compared to that arising from purely classical dynamics. Furthermore, in the nearly adiabatic regime the efficiency of the refrigerator exceeds clearly that of the standard Otto cycle.
Quantum refrigerators (QRs) are pivotal in exploring thermodynamic behavior at microscopic scales. This study investigates a quantum Otto refrigerator using a bosonic gas confined in a cubic potential, operating under finite-time thermalization. We derive key thermodynamic quantities analytically, including the coefficient of performance (COP), cooling power, entropy, and cooling rate. Additionally, we investigate how partial thermalization during the isochoric heating and cooling stages influences overall system performance. The findings reveal a trade-off between COP and cooling power, emphasizing the importance of thermalization duration. Notably, by extending the cooling time relative to heating, the COP can be significantly improved, offering a practical approach to optimizing QR performance under realistic conditions.
In this work we considered the quantum Otto cycle within an optimization framework. The goal was maximizing the power for a heat engine or maximizing the cooling power for a refrigerator. In the field of finite-time quantum thermodynamics it is common to consider frictionless trajectories since these have been shown to maximize the work extraction during the adiabatic processes. Furthermore, for frictionless cycles, the energy of the system decouples from the other degrees of freedom, thereby simplifying the mathematical treatment. Instead, we considered general limit cycles and we used analytical techniques to compute the derivative of the work production over the whole cycle with respect to the time allocated for each of the adiabatic processes. By doing so, we were able to directly show that the frictionless cycle maximizes the work production, implying that the optimal power production must necessarily allow for some friction generation so that the duration of the cycle is reduced.