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arXiv:2210.00250 · Chinese Physics B

Quantum Stirling heat engine with squeezed thermal reservoir

Nikolaos Papadatos

Published Mar 28, 2023• 13 citations
arXivHTMLPDF

Abstract

We analyze the performance of a quantum Stirling heat engine (QSHE), using a two-level system and a harmonic oscillator as the working medium, that is in contact with a squeezed thermal reservoir and a cold reservoir. First, we derive closed-form expressions for the produced work and efficiency, which strongly depend on the squeezing parameter r h. Then, we prove that the effect of squeezing heats the working medium to a higher effective temperature, which leads to better overall performance. In particular, the efficiency increases with the degree of squeezing, surpassing the standard Carnot limit when the ratio of the temperatures of the hot and cold reservoirs is small. Furthermore, we derive the analytical expressions for the efficiency at maximum work and the maximum produced work in the high and low temperature regimes, and we find that at extreme temperatures the squeezing parameter r h does not affect the performance of the QSHE. Finally, the performance of the QSHE depends on the nature of the working medium.

DOI
10.1088/1674-1056/acc7f8

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We analyze the performance of a quantum Stirling heat engine (QSHE), using a two-level system and a harmonic oscillator as the working medium, that is in contact with a squeezed thermal reservoir and a cold reservoir. First, we derive closed-form expressions for the produced work and efficiency, which strongly depend on the squeezing parameter r h. Then, we prove that the effect of squeezing heats the working medium to a higher effective temperature, which leads to better overall performance. In particular, the efficiency increases with the degree of squeezing, surpassing the standard Carnot limit when the ratio of the temperatures of the hot and cold reservoirs is small. Furthermore, we derive the analytical expressions for the efficiency at maximum work and the maximum produced work in the high and low temperature regimes, and we find that at extreme temperatures the squeezing parameter r h does not affect the performance of the QSHE. Finally, the performance of the QSHE depends on the nature of the working medium.
We propose a quantum Stirling heat engine with an ensemble of harmonic oscillators as the working medium. We show that the efficiency of the harmonic oscillator quantum Stirling heat engine (HO-QSHE) at a given frequency can be maximized at a specific ratio of the temperatures of the thermal reservoirs. In the low-temperature or equivalently high-frequency limit of the harmonic oscillators, the efficiency of the HO-QSHE approaches the Carnot efficiency. Further, we analyze a quantum Stirling heat engine with an ensemble of particle-in-a-box quantum systems as the working medium. Here both work and efficiency can be maximized at a specific ratio of temperatures of the thermal reservoirs. These studies will enable us to operate the quantum Stirling heat engines at its optimal performance. The theoretical study of the HO-QSHE would provide impetus for its experimental realization, as most real systems can be approximated as harmonic oscillators for small displacements near equilibrium.
Enhancing the efficiency of quantum heat engines (QHEs) is crucial for advancing fundamental research and quantum technology.We here we explore a quantum Stirling cycle using a twoqubit quantum Rabi model with spin-spin coupling as a working medium. We propose parameter optimization strategies to maximize the efficiency of the heat engine, as there are multiple ways for the effective coupling constant to move toward its critical value. In the normal phase of the system, the efficiency can be improved by increasing the temperature ratio of hot-to-cold reservoirs and enhancing spin-mode coupling strength. However, increasing spin-spin coupling strength inhibits the improvement of the efficiency. As the system goes to its critical point, QHE efficiency under low-temperature conditions tends to the Carnot limit. In the superradiant phase, the efficiency approaches the Carnot limit more closely as the cold reservoir's temperature decreases given a constant temperature ratio. Conversely, when the cold reservoir's temperature rises, the efficiency increases due to a higher ratio of spin-mode coupling strength to mode frequency. If the spinspin coupling strength is constant, increasing the hot-to-cold reservoir temperature ratio requires a corresponding increase in spin-mode coupling strength to achieve the Carnot efficiency. Our work deepens the understanding of QHE performance under various conditions and provides operative methods for optimizing the efficiency of QHE.
Abstract We work on a comprehensive theoretical investigation of a three-level quantum heat engine operating with engineered squeezed thermal reservoirs. Unlike conventional quantum heat engines that use thermal reservoirs, we demonstrate that squeezed reservoirs can significantly enhance the engine's performance by increasing both efficiency and output power. Using a rigorous open-quantum-system approach, we derive the full Lindblad master equation for a three-level system interacting with hot and cold squeezed thermal baths. Through a detailed analysis of the steady-state thermodynamics, we obtain explicit expressions for heat currents, work output, and efficiency. Our results reveal that moderate squeezing parameters (r≈0.5r \approx 0.5r≈0.5) combined with optimal squeezing phase (ϕ=π/2\phi = \pi/2ϕ=π/2) enhance the engine efficiency by up to 40\% compared to the classical Carnot limit for the same temperature ratio. The power output shows a non-monotonic behavior with squeezing, exhibiting an optimal squeezing parameter that maximizes performance. We identify three distinct operational regimes: (i) heat engine regime, (ii) refrigerator regime, and (iii) heat pump regime, which can be tuned by adjusting the squeezing phase. The efficiency at maximum power follows a universal scaling ηMP≈ηCarnot/2+Δη(r)\eta_{MP} \approx \eta_{Carnot}/2 + \Delta\eta(r)ηMP​≈ηCarnot​/2+Δη(r), where Δη(r)\Delta\eta(r)Δη(r) represents the squeezing-induced enhancement. Our findings provide fundamental insights into the role of non-thermal reservoirs in quantum thermodynamics and offer practical guidelines for designing high-performance quantum heat engines using squeezed light and engineered baths.
We analyze the performance of a quantum Otto cycle, employing a time-dependent harmonic oscillator as the working fluid undergoing sudden expansion and compression strokes during the adiabatic stages, coupled to a squeezed reservoir. First, we show that the maximum efficiency that our engine can achieve is 1/2 only, which is in contrast with earlier studies claiming unit efficiency under the effect of a squeezed reservoir. Then, in the high-temperature limit, we obtain analytic expressions for the upper bound on the efficiency as well as on the coefficient of performance of the Otto cycle. The obtained bounds are independent of the parameters of the system and depend on the reservoir parameters only. Additionally, with a hot squeezed thermal bath, we obtain an analytic expression for the efficiency at maximum work which satisfies the derived upper bound. Further, in the presence of squeezing in the cold reservoir, we specify an operational regime for the Otto refrigerator otherwise forbidden in the standard case. Finally, we find the cost of creating a squeezed state from the thermal state and show that in order to harvest the benefits of squeezing, it is sufficient to squeeze only one mode of the reservoir in resonance with the transition frequency of the working fluid. Further, we show that when the cost of squeezing is included in the definition of the operational efficiency of the engine, the advantages of squeezing fade away. Still, being purely quantum mechanical fuel in nature, squeezed reservoirs are beneficial in their own way by providing us with more compact energy storage medium or offering effectively high-temperature baths without being actually too hot.
We consider the finite-time performance of a quantum Otto engine working between a hot squeezed and a cold thermal bath at inverse temperatures ${\ensuremath{\beta}}_{h}$ and ${\ensuremath{\beta}}_{c}(>{\ensuremath{\beta}}_{h})$ with $({k}_{B}\ensuremath{\equiv}1)\ensuremath{\beta}=1/T$. We derive the analytical expressions for work, efficiency, power, and power fluctuations, in which the squeezing parameter is involved. By optimizing the power output with respect to two frequencies, we derive the efficiency at maximum power as ${\ensuremath{\eta}}_{mp}={({\ensuremath{\eta}}_{C}^{\mathrm{gen}})}^{2}/[{\ensuremath{\eta}}_{C}^{\mathrm{gen}}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C}^{\mathrm{gen}})ln(1\ensuremath{-}{\ensuremath{\eta}}_{C}^{\mathrm{gen}})]$, where the generalized Carnot efficiency ${\ensuremath{\eta}}_{C}^{\mathrm{gen}}$ in the high-temperature or small squeezing limit simplifies to an analytic function of squeezing parameter $\ensuremath{\gamma}$: ${\ensuremath{\eta}}_{C}^{\mathrm{gen}}=1\ensuremath{-}{\ensuremath{\beta}}_{h}/[{\ensuremath{\beta}}_{c}cosh(2\ensuremath{\gamma})]$. Within the context of irreversible thermodynamics, we demonstrate that the expression of efficiency at maximum power satisfies a general form derived from nonlinear steady state heat engines. We show that, the power fluctuations are considerably increased, although the engine efficiency is enhanced by squeezing.
In a quantum Stirling heat engine, the heat exchanged with two thermal baths is partly utilized for performing work by redistributing the energy levels of the working substance. We analyze the thermodynamics of a quantum Stirling engine operating in finite time. We develop a model in which a time-dependent potential barrier changes the energy-level structure of the working substance. The process takes place under a constant interaction with the thermal bath. We further show that in the limit of slow operation of the cycle and low temperature, the efficiency of such an engine approaches Carnot efficiency. We also show that the maximum output power, for the strokes that affect the energy levels, is obtained at an intermediate operating speed, demonstrating the importance of a finite-time analysis.