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.
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.
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.
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.
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.
We discuss whether, and under which conditions, it is possible to realize a heat engine simply by dynamically modulating the couplings between the quantum working medium and thermal reservoirs. For that purpose, we consider the paradigmatic model of a quantum harmonic oscillator, exposed to a minimal modulation, that is, a monochromatic driving of the coupling to only one of the thermal baths. We demonstrate, at any order in the system/bath coupling strength, that in this setup non-Markovianity of the bath is a necessary condition to obtain a heat engine. In addition, we identify suitable structured environments for the engine to approach the ideal Carnot efficiency. Our results open up new possibilities for the use of non-Markovian open quantum systems for the construction and optimization of quantum thermal machines.
Abstract We study the thermodynamic performance of a finite-time non-regenerative quantum Stirling-like cycle used as a heat engine. We consider specifically the case in which the working substance (WS) is a two-level system (TLS). The Stirling cycle is made of two isochoric transformations separated by a compression and an expansion stroke during which the WS is in contact with a thermal reservoir. To describe these two strokes we derive a non-Markovian master equation which allows to study the real-time dynamics of a driven open quantum system with arbitrary fast driving. Following the real-time dynamics of the WS using this master equation, the endpoints of the isotherms can deviate from the equilibrium thermal states. The role of this deviation in the performance of the heat engine is addressed. We found that the finite-time dynamics and thermodynamics of the cycle depend non-trivially on the different time scales at play. In particular, driving the WS at a time scale comparable to the resonance time of the bath enhances the performance of the cycle and allows for an efficiency higher than the efficiency of the quasistatic cycle, but still below the Carnot bound. However, by adding thermalization of the WS with the baths at the end of compression/expansion processes one recovers the conventional scenario in which efficiency decreases by speeding up the processes. In addition, the performance of the cycle is dependent on the compression/expansion speeds asymmetrically, which suggests new freedom in optimizing quantum heat engines. The maximum output power and the maximum efficiency are obtained almost simultaneously when the real-time endpoints of the compression/expansion processes are considered instead of the equilibrium thermal endpoint states. However, the net extractable work always declines by speeding up the drive.
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.