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arXiv:2312.12350 · Physical review. E

Work and efficiency fluctuations in a quantum Otto cycle with idle levels

Maron F. Anka, Thiago R. de Oliveira, Daniel Jonathan

Published Jun 13, 2024• 2 citations
arXivHTMLPDF

Abstract

We study the performance of a quantum Otto heat engine with two spins coupled by a Heisenberg interaction, taking into account not only the mean values of work and efficiency but also their fluctuations. We first show that, for this system, the output work and its fluctuations are directly related to the magnetization and magnetic susceptibility of the system at equilibrium with either heat bath. We analyze the regions where the work extraction can be done with low relative fluctuation for a given range of temperatures, while still achieving an efficiency higher than that of a single spin system heat engine. In particular, we find that, due to the presence of "idle" levels, an increase in the interspin coupling can either increase or decrease fluctuations, depending on the other parameters. In all cases, however, we find that the relative fluctuations in work or efficiency remain large, implying that this microscopic engine is not very reliable as a source of work.

DOI
10.1103/physreve.109.064129

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We study the performance of a quantum Otto heat engine with two spins coupled by a Heisenberg interaction, taking into account not only the mean values of work and efficiency but also their fluctuations. We first show that, for this system, the output work and its fluctuations are directly related to the magnetization and magnetic susceptibility of the system at equilibrium with either heat bath. We analyze the regions where the work extraction can be done with low relative fluctuation for a given range of temperatures, while still achieving an efficiency higher than that of a single spin system heat engine. In particular, we find that, due to the presence of "idle" levels, an increase in the interspin coupling can either increase or decrease fluctuations, depending on the other parameters. In all cases, however, we find that the relative fluctuations in work or efficiency remain large, implying that this microscopic engine is not very reliable as a source of work.
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.
In this work we study the effect of quantum and thermal fluctuations on the statistics of quantum heat engine performance parameters, like efficiency and power. We begin by deriving an explicit solution for the characteristic function of the heat distribution of a thermal quantum harmonic oscillator. We then derive a general framework based on the standard two-point-measurement scheme to compute the efficiency distribution of a quantum Otto cycle. We analyze the generic properties of this distribution for scale-invariant driving Hamiltonians which describe a large class of single-particle, many-body, and nonlinear systems. We find that the efficiency is deterministic and that its mean is equal to the macroscopic efficiency for adiabatic driving. We continue our research by studying the efficiency large deviation function of two exemplary quantum heat engines, the harmonic oscillator and the two-level Otto cycles. While the efficiency statistics follow the ’universal’ theory of Verley et al. [Nature Commun. 5, 4721 (2014)] for nonadiabatic driving, we find that the latter framework does not apply in the adiabatic regime. We can relate this unusual property to the perfect anticorrelation between work output and heat input that suppresses thermal as well as quantum fluctuations. We then probe our findings in an experimental NMR setup using spin-1/2 systems and find them to agree rather well with our theoretical predictions. Afterward, we move on to the finite-time quantum Carnot cycle and investigate its power fluctuations. In particular, we consider how level degeneracy and level number, two commonly found properties in quantum systems, influence the relative work fluctuations. We find that their optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results highlight that these parameters can be employed to realize high-performance, high-stability cyclic quantum heat engines.
A properly selected quantum heat engine consumes resources efficiently. Also, there are many parameters to determine the right option. In this study, we construct and compare the quantum mechanical counterparts of Stirling and Otto cycles for an experimentally achievable quantum working medium where two spins 1/2 interact through isotropic Heisenberg interaction in the tunable external magnetic field. We consider two comparison cases that operate heat cycles with the same system parameters or equal efficiencies. The quantum Stirling cycle produces more work than that of the Otto cycle under the same parameters or equal efficiency conditions. The quantum Stirling engine operates a wider range of coupling strengths. The work performed in the cycles is enhanced by coupling strength. On the other hand, we investigate the role of coupling strength on the performance of the non-regenerative quantum Stirling heat cycle under various magnitudes of the magnetic field. The distance between the applied magnetic fields at the initial and final points of the isothermal stage is found to be an enhancer for the work output and efficiency of the quantum Stirling cycle.
We compare quantum Otto engines based on two different cycle models: a two-bath model, with a standard heat source and sink, and a measurement-based protocol, where the role of heat source is played by a quantum measurement. We furthermore study these cycles using two different "working substances": a single qutrit (spin-1 particle) or a pair of qubits (spin-1/2 particles) interacting via the XXZ Heisenberg interaction. Although both cycle models have the same efficiency when applied on a single-qubit working substance, we find that both can reach higher efficiencies using these more complex working substances by exploiting the existence of "idle" levels, i.e., levels that do not shift while the spins are subjected to a variable magnetic field. Furthermore, with an appropriate choice of measurement, the measurement-based protocol becomes more efficient than the two-bath model.
Abstract We start with a revision study of two coupled spin- 1 / 2 under the influence of Kaplan–Shekhtman–Entin-Wohlman–Aharony interaction and a magnetic field. We first show the role of idle levels, i.e. levels that do not couple to the external magnetic field, when the system is working as a heat engine as well as when it is a refrigerator. Then we extend the results reported in Altintas and Müstecaplıoğlu (2015 Phys. Rev. E 92 022142) by showing that it is not necessary to change both the magnetic field as well as the coupling parameters to break the extensive property of the work extracted globally from two coupled spin- 1 / 2 as has been demonstrated there. Then we study the role of increasing the number of coupled spins on efficiency, extractable work, and coefficient of performance (COP). First, we consider two- and three-coupled spin- 1 / 2 Heisenberg X X X -chain. We prove that the latter can outperform the former in terms of efficiency, extractable work, and COP. Then we consider the Ising model, where the number of interacting spins ranges from two to six. We show that only when the number of interacting spins is odd the system can work as a heat engine in the strong coupling regime. The enhancements in efficiency and COP are explored in detail. Finally, this model confirms the idea that entanglement and quantum correlations are not the reasons behind the enhancements observed in efficiency, extractable work, and COP, but only due to the structure of the energy levels of the Hamiltonian of the working substance. In addition to this, the extensive property of global work as well, is not affected by entanglement and quantum correlations.
Abstract The thermodynamic properties of quantum heat engines are stochastic owing to the presence of thermal and quantum fluctuations. We here experimentally investigate the efficiency and nonequilibrium entropy production statistics of a spin-1/2 quantum Otto cycle in a nuclear magnetic resonance setup. We first study the correlations between work and heat within a cycle by extracting their joint distribution for different driving times. We show that near perfect correlation, corresponding to the tight-coupling condition between work and heat, can be achieved. In this limit, the reconstructed efficiency distribution is peaked at the deterministic thermodynamic efficiency, and fluctuations are strongly suppressed. We further successfully test the second law in the form of a joint fluctuation relation for work and heat in the quantum cycle. Our results characterize the statistical features of a small-scale thermal machine in the quantum domain, and provide means to control them.