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Physica Scripta

Efficiency of the non-maximally entangled quantum Otto engine

Heru Sukamto, Lila Yuwana, Agus Purwanto, Sithi Vinayakam Muniandy

Published Feb 23, 2024• 2 citations
Publisher

Abstract

Abstract We generalized the maximally entangled Hamiltonian of the isotropic Heisenberg XX model with two spin-1/2 particles to the case of non-maximal entanglement parametrized by the degree of non-maximality 0 < n < 1. The thermal concurrence as the function of the degree of non-maximality in the entanglement at different values of the exchange parameter is calculated. We analyzed the efficiency of the quantum Otto engine for different scenarios of exchange parameter regimes and the degree of maximal entanglement between the spin states. We showed that it is possible to run the quantum Otto engine using non-maximally entangled states and achieve higher efficiencies by controlling the exchange parameter value with respect to a critical value J c and this feature also depends on the degree of non-maximal entanglement n ≠ 1. This result may be useful for harnessing the non-maximal entanglement in quantum heat engine for optimizing the operation of quantum devices interacting with heat bath or environment.

DOI
10.1088/1402-4896/ad2cd1

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Abstract We generalized the maximally entangled Hamiltonian of the isotropic Heisenberg XX model with two spin-1/2 particles to the case of non-maximal entanglement parametrized by the degree of non-maximality 0 < n < 1. The thermal concurrence as the function of the degree of non-maximality in the entanglement at different values of the exchange parameter is calculated. We analyzed the efficiency of the quantum Otto engine for different scenarios of exchange parameter regimes and the degree of maximal entanglement between the spin states. We showed that it is possible to run the quantum Otto engine using non-maximally entangled states and achieve higher efficiencies by controlling the exchange parameter value with respect to a critical value J c and this feature also depends on the degree of non-maximal entanglement n ≠ 1. This result may be useful for harnessing the non-maximal entanglement in quantum heat engine for optimizing the operation of quantum devices interacting with heat bath or environment.
Based on the isotropic two spin-1/2 qubits Heisenberg model with Dzyaloshinskii–Moriya interaction in a constant external magnetic field, we have constructed the entangled quantum Otto engine. Expressions for the basic thermodynamic quantities, i.e. the amount of heat exchange, the net work output and the efficiency, are derived. The influence of thermal entanglement on these basic thermodynamic quantities is investigated. Moreover, some intriguing features and their qualitative explanations in zero and finite magnetic field are given. The validity of the second law of thermodynamics is confirmed in the system. The results obtained here have general significance and will be useful in increasing understanding of the performance of an entangled quantum engine.
This paper establishes an entangled otto quantum heat engine(EQHE) working with the two-qubit anisotropic Heisenberg XXZ model.Based on the first law of quantum thermodynamics,we derive the expressions for the net work and the efficiency of EQHE.By numerical calculation we plot three dimensional graphics between the efficiency and the concurrence.It is found that the efficiency of the EQHE is smaller than the Carnot efficiency and the validity of the second law of thermodynamics is confirmed;The region of non-zero efficiency is mainly distributed in C1C2 and the value of efficiency and region of non-zero efficiency increase with the increase of the ratio of the temperature γ.The efficiency of the EQHE is discussed in two special cases Δ=0 and Δ=1.
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.
We construct a special four-level entangled quantum Otto heat engine based on the two-qubit Heisenberg XX model, in which we assume that all the energy gaps are changed in the same ratio in the two quantum adiabatic processes. Hence during the whole cycle, the relative coupling constant κ = J / B is fixed, where J and B are the coupling constant and the external magnetic field, respectively. The dependence of the basic thermodynamical quantities on the two entanglements at the end of two quantum isochoric processes with different relative coupling constants κ is studied. Our results show that in the weak coupling region, i.e. κ < 1, the heat engine can be operated in both areas where c 1 < c 2 and c 1 > c 2 , whereas when κ ⩾ 1, it only operates under the condition c 1 < c 2 . Here c 1 and c 2 are entanglements of the working substance when it comes into contact with hot and cold baths, respectively. Moreover, we find that the maximal work output for fixed κ increases with the relative coupling constant.
The four-level entangled quantum heat engine (QHE) is analyzed in the various Heisenberg models for a two-qubit. The QHE is examined for the XX, XXX and XXZ Heisenberg models by introducing a parameter x which controls the strength of the exchange parameter Jz = xJ along the z-axis with respect to the ones along the x- and y-axes, i.e. Jx = Jy = J, respectively. It is assumed that the two-qubit is entangled and in contact with two heat reservoirs at different temperatures and under the effect of a constant magnetic field. The concurrences (C) are used as a measure of entanglement and then the expressions for the amount of heat transferred, the work performed and the efficiency of the QHE are derived. The contour, i.e. the isoline maps, and some two-dimensional plots of the above mentioned thermodynamic quantities are calculated and some interesting features are found.
We study a quantum Otto heat engine whose working substance is an anisotropic two-qubit Heisenberg XYZ model. Independent local magnetic fields are used to control each spin individually. The influence of the longitudinal coupling, anisotropy, transverse coupling, and local fields on the net work output and efficiency is systematically examined. Reducing the longitudinal coupling is found to markedly improve both the maximum work and the peak efficiency. The engine performance reaches an optimum at a particular value of the anisotropy parameter. A local work analysis clarifies how work is produced during the cycle. Because of the asymmetric local fields and the intrinsic spin-spin interaction, the two qubits play markedly different thermodynamic roles; the interaction term itself contributes crucially to the total work. We further analyze the variation of quantum entanglement, quantified by concurrence, along the cycle. The results indicate that a pronounced change in entanglement between the hot and cold isomagnetic strokes is closely correlated with the efficiency enhancement. This work offers new insight into the operating principles and control of quantum Otto heat engines.