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arXiv:2102.11657 · TURKISH JOURNAL OF PHYSICS

Finite-time two-spin quantum Otto engines: Shortcuts to adiabaticity vs. irreversibility

Barış Çakmak

Published Feb 26, 2021• 10 citations
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Abstract

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.

DOI
10.3906/fiz-2101-10

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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 consider a finite-time quantum Otto cycle with single- and two spin-1/2 systems as its working medium. To mimic adiabatic dynamics at a finite time, we employ a shortcut-to-adiabaticity technique and evaluate the performance of the engine including the cost of the shortcut. We compare our results with the true adiabatic and nonadiabatic performances of the same cycle. Our findings indicate that the use of the shortcut-to-adiabaticity scheme significantly enhances the performance of the quantum Otto engine as compared to its adiabatic and nonadiabatic counterparts for different figures of merit.
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.
The finite time operation of a quantum Otto heat engine leads to a trade-off between efficiency and output power, which is due to the deviation of the system from the adiabatic path. This trade-off caveat can be bypassed by using the shortcut-to-adiabaticity protocol. We experimentally implemented a quantum Otto heat engine using spin-1/2 nuclei on a nuclear magnetic resonance (NMR) quantum processor. We investigated its performance using the shortcut-to-adiabaticity technique via counter-adiabatic driving with the inclusion of the cost to perform the shortcut. We use two different metrics that incorporate the cost of shortcut-to-adiabaticity to define engine efficiency and experimentally analyze which one is more appropriate for the NMR platform. We found a significant improvement in the performance of the quantum Otto heat engine driven by shortcut-to-adiabaticity, as compared to the non-adiabatic heat engine.
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.
We have studied the performance of a measurement-based quantum Otto engine (QOE) in a working system of two spins coupled by Heisenberg anisotropic interaction. A nonselective quantum measurement fuels the engine. We have calculated thermodynamic quantities of the cycle in terms of the transition probabilities between the instantaneous energy eigenstates, and also between the instantaneous energy eigenstates and the basis states of the measurement, when the unitary stages of the cycle operate for a finite time τ. The efficiency attains a large value in the limit of τ→0 and then gradually reaches the adiabatic value in a long-time limit τ→∞. For finite values of τ and for anisotropic interaction, an oscillatory behavior of the efficiency of the engine is observed. This oscillation can be interpreted in terms of interference between the relevant transition amplitudes in the unitary stages of the engine cycle. Therefore, for a suitable choice of timing of the unitary processes in the short time regime, the engine can have a higher work output and less heat absorption, such that it works more efficiently than a quasistatic engine. In the case of an always-on heat bath, in a very short time, the bath has a negligible effect on its performance.
The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum heat engine utilizing a many-particle working medium in combination with the use of shortcuts to adiabaticity to boost the nonadiabatic performance by eliminating quantum friction and reducing the cycle time. To this end, we first analyze the finite-time thermodynamics of a quantum Otto cycle implemented with a quantum fluid confined in a time-dependent harmonic trap. We show that nonadiabatic effects can be controlled and tailored to match the adiabatic performance using a variety of shortcuts to adiabaticity. As a result, the nonadiabatic dynamics of the scaled-up many-particle quantum heat engine exhibits no friction, and the cycle can be run at maximum efficiency with a tunable output power. We demonstrate our results with a working medium consisting of particles with inverse-square pairwise interactions that includes non-interacting and hard-core bosons as limiting cases.