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Journal of Physics B Atomic Molecular and Optical Physics

Shortcut-to-adiabaticity quantum tripartite Otto cycle

Lunan Li, Hai Li, Wen-Li Yu, Yaming Hao, Lei Li, Jian Zou

Published Nov 3, 2021• 8 citations

Abstract

Abstract For an Otto cycle there always exists a trade-off between the cycle efficiency and the output power due to the requirement of cycle length. The shortcut to adiabatic (STA) technology provides an effective way to deal with the difficulty of zero-output power in conventional Otto cycle. In this paper, the Otto cycle of three-qubit system as the working substance with counterdiabatic driving has been investigated. It is demonstrated that the tripartite Otto cycle as a universal machine, in the suitable regimes of external control parameter, could work as a quantum heat engine (QHE), refrigerator or heat pump. And, the performances of QHE and refrigerator with and without STA, such as the power and efficiency of QHE and the coefficient of performance (COP) and figure of merit (FOM) of refrigerator, have been investigated. It shows the application of STA scheme can lead to an effective enhancement in the performances of Otto cycle, including achievements of a high QHE’s/refrigerator’s power associated with a moderate QHE’s efficiency/COP of refrigerator. Especially, it is interesting that even in a short-time cycle the optimization of control parameters could arise a remarkable improvement in the efficiency (or COP) of STA QHE (refrigerator), approaching the ideal efficiency or COP of conventional Otto cycle with quasi-static process. Finally, with the aid of parameter optimization the trade-off regions between the efficiency and the power (the COP and the FOM) of STA Otto engine (refrigerator) have been advised.

DOI: 10.1088/1361-6455/ac3c93

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We propose a quantum Otto cycle in a two spin-1/2 anisotropic XY model in a transverse external magnetic field. We first characterize the parameter regime that the working medium operates as an engine in the adiabatic regime. Then, we consider finite-time behavior of the engine with and without utilizing a shortcut to adiabaticity (STA) technique. STA schemes guarantee that the dynamics of a system follows the adiabatic path, at the expense of introducing an external control. We compare the performance of the nonadiabatic and STA engines for a fixed adiabatic efficiency but different parameters of the working medium. We observe that, for certain parameter regimes, the irreversibility, as measured by the efficiency lags, due to finite-time driving is so low that nonadiabatic engine performs quite close to the adiabatic engine, leaving the STA engine only marginally better than the nonadiabatic one. This suggests that by designing the working medium Hamiltonian one may spare the difficulty of dealing with an external control protocol.

We investigate the performance of a quantum Otto refrigerator operating in finite time and exploiting local counterdiabatic techniques. We evaluate its coefficient of performance and cooling power when the working medium consists of a quantum harmonic oscillator with a time-dependent frequency. We find that the quantum refrigerator outperforms its conventional counterpart, except for very short cycle times, even when the driving cost of the local counterdiabatic driving is included. We moreover derive upper bounds on the performance of the thermal machine based on quantum speed limits and show that they are tighter than the second law of thermodynamics.

We consider a paradigmatic quantum harmonic Otto engine operating in finite time. We investigate its performance when shortcut-to-adiabaticity techniques are used to speed up its cycle. We compute efficiency and power by taking the energetic cost of the shortcut driving explicitly into account. We analyze in detail three different shortcut methods: counterdiabatic driving, local counterdiabatic driving, and inverse engineering. We demonstrate that all three lead to a simultaneous increase of efficiency and power for fast cycles, thus outperforming traditional heat engines.

Abstract We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater.

In this work we investigate a finite-time quantum Otto-like heat engine with a single-qubit working substance, distinguished from the standard Otto cycle by introducing a unitary operation before the cold isochore. This operation suppresses the slowest decaying mode of the open-system dynamics and broadens the spectral gap, thereby inducing an exponential to accelerate the subsequent thermalization process toward stationarity. We derive analytic expressions for the work, heat, and efficiency, and perform numerical simulations comparing the standard Otto engine, the shortcut to adiabatic engine, and our proposed Otto-like engine. Our analysis demonstrates that with an appropriate parameter selection, the additional unitary operation can significantly boost the system's power and efficiency. Finally, using the unified optimization criterion Φ, we further show that the modified cycle consistently outperforms both the conventional cycle and the shortcut to adiabatic protocol.