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arXiv:1810.07161 · Entropy

Measurement Based Quantum Heat Engine with Coupled Working Medium

Arpan Das, Sibasish Ghosh

Published Nov 19, 2019• 34 citations
arXivHTMLPDF

Abstract

We consider measurement based single temperature quantum heat engine without feedback control, introduced recently by Yi, Talkner and Kim [Phys. Rev. E 96, 022108 (2017)]. Taking the working medium of the engine to be a one-dimensional Heisenberg model of two spins, we calculate the efficiency of the engine undergoing a cyclic process. Starting with two spin-1/2 particles, we investigate the scenario of higher spins also. We show that, for this model of coupled working medium, efficiency can be higher than that of an uncoupled one. However, the relationship between the coupling constant and the efficiency of the engine is rather involved. We find that in the higher spin scenario efficiency can sometimes be negative (this means work has to be done to run the engine cycle) for certain range of coupling constants, in contrast to the aforesaid work of Yi, Talkner and Kim, where they showed that the extracted work is always positive in the absence of coupling. We provide arguments for this negative efficiency in higher spin scenarios. Interestingly, this happens only in the asymmetric scenarios, where the two spins are different. Given these facts, for judiciously chosen conditions, an engine with coupled working medium gives advantage for the efficiency over the uncoupled one.

DOI
10.3390/e21111131

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We consider measurement based single temperature quantum heat engine without feedback control, introduced recently by Yi, Talkner and Kim [Phys. Rev. E 96, 022108 (2017)]. Taking the working medium of the engine to be a one-dimensional Heisenberg model of two spins, we calculate the efficiency of the engine undergoing a cyclic process. Starting with two spin-1/2 particles, we investigate the scenario of higher spins also. We show that, for this model of coupled working medium, efficiency can be higher than that of an uncoupled one. However, the relationship between the coupling constant and the efficiency of the engine is rather involved. We find that in the higher spin scenario efficiency can sometimes be negative (this means work has to be done to run the engine cycle) for certain range of coupling constants, in contrast to the aforesaid work of Yi, Talkner and Kim, where they showed that the extracted work is always positive in the absence of coupling. We provide arguments for this negative efficiency in higher spin scenarios. Interestingly, this happens only in the asymmetric scenarios, where the two spins are different. Given these facts, for judiciously chosen conditions, an engine with coupled working medium gives advantage for the efficiency over the uncoupled one.
Study of coupled quantum systems as quantum heat engines is an interesting research area. It has been shown earlier that coupling can increase the efficiency. Here we make a comparative study between coupled spin-1/21/21/2 systems and coupled quantum oscillators when they constitute as the working medium of a quantum heat engine. For this purpose, we consider anisotropic 1-D Heisenberg model of interaction between two spin-1/21/21/2 systems. Analogous interaction in the case of two oscillators is realized by considering quadratic coupling between positions and momenta of the two oscillators. Interestingly, we point out certain range of parameters for which the efficiency of the coupled oscillators outperform the efficiency obtained from coupled spin systems. It happens that with suitable co-ordinate transformation, the coupled system appears to be uncoupled in the new frame of reference. We show that the global efficiency of the total system is bounded (both from above and below) by the efficiencies of the independent systems, provided both the independent systems work in the engine mode. When the upper bound of the efficiency becomes Carnot efficiency, then the global efficiency reaches the lower bound. The global efficiency further decreases when one of the independent systems works as a refrigerator.
Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.
This paper investigates a coupled two-qubits heat engine fueled by generalized measurements of the spin components and using a single heat reservoir as sink. Our model extends the proposal of Yi, Talkner, and Kim [Phys. Rev. E 96, 022108 (2017)2470-004510.1103/PhysRevE.96.022108], where the role of a hot reservoir in a four-stroke cycle was replaced by a quantum measurement apparatus, the other steps being two quantum adiabatic strokes and thermalization with a cold reservoir. We propose a five-stroke cycle, where an ergotropy extracting stroke is introduced following the measurement stroke, and study the effect of measurements of different spin components on the performance of the machine. For measurements along z-z directions, we find two possible occupation distributions that yield an active state and the ergotropic stroke improves the performance of the engine over the four-stroke cycle. Further, the three-stroke engine (without the adiabatic strokes) yields the same performance as the five-stroke engine. For arbitrary working medium and nonselective measurements, we prove that the total work output of a five-stroke engine is equal to the sum of the work outputs of the corresponding four-stroke and three-stroke engines. For measurement directions other than z-z, there may be many possible orderings of the postmeasurement probabilities that yield an active state. However, as we illustrate, for specific cases (e.g., x-x), a definite ordering may be obtained with the projective measurements. Thus we find that the five-stroke engine exploiting ergotropy outperforms both its four-stroke as well as three-stroke counterparts.
We study the one-dimensional isotropic Heisenberg model of two spin-1/2 systems as a quantum heat engine. The engine undergoes a four-step Otto cycle where the two adiabatic branches involve changing the external magnetic field at a fixed value of the coupling constant. We find conditions for the engine efficiency to be higher than in the uncoupled model; in particular, we find an upper bound which is tighter than the Carnot bound. A domain of parameter values is pointed out which was not feasible in the interaction-free model. Locally, each spin seems to cause a flow of heat in a direction opposite to the global temperature gradient. This feature is explained by an analysis of the local effective temperature of the spins.
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.
We introduce a new quantum heat engine, in which the working medium undergoes quantum quasi-adiabatic and non-unitary processes to extract work in the cycle. Two kinds of working medium are considered. The first one consists of a three-level quantum system, whereas the second is a quantum system with a discrete level and a continuum. Net work done by this engine is calculated and discussed. The results show that this quantum heat engine behaves like the two-level quantum heat engine in both the high-temperature and low-temperature limits, but it operates differently at intermediate temperatures. The efficiency of this quantum heat engine is also presented and discussed.