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Physical Review A

Four-level entangled quantum heat engines

Ting Zhang, Wei-Tao Liu, Ping‐Xing Chen, Cheng-Zu Li

Published Jun 5, 2007• 145 citations
Publisher

Abstract

Based on a two-qubit one-dimensional isotropic spin-$1∕2$ Heisenberg spin chain in a constant external magnetic field, we construct a four-level entangled quantum heat engine (QHE) and investigate the influence of entanglement between two qubits on basic thermodynamic quantities, i.e., the heat transferred and the work done in a cycle, and the efficiency of the QHE. The validity of the second law of thermodynamics is confirmed in the entangled system. We also find several interesting features of the variation of the efficiency with the entanglement of two different thermal equilibrium states in a work cycle in zero and finite magnetic field. An abrupt transition of efficiency is found in zero field.

DOI
10.1103/physreva.75.062102

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Based on a two-qubit one-dimensional isotropic spin-1∕21∕21∕2 Heisenberg spin chain in a constant external magnetic field, we construct a four-level entangled quantum heat engine (QHE) and investigate the influence of entanglement between two qubits on basic thermodynamic quantities, i.e., the heat transferred and the work done in a cycle, and the efficiency of the QHE. The validity of the second law of thermodynamics is confirmed in the entangled system. We also find several interesting features of the variation of the efficiency with the entanglement of two different thermal equilibrium states in a work cycle in zero and finite magnetic field. An abrupt transition of efficiency is found in zero field.
Based on a two-qubit isotropic Heisenberg XY model under a constant external magnetic field, we construct a four-level entangled quantum heat engine (QHE). The expressions for the heat transferred, the work, and the efficiency are derived. Moreover, the influence of the entanglement on the thermodynamic quantities is investigated analytically and numerically. Several interesting features of the variations of the heat transferred, the work, and the efficiency with the concurrences of the thermal entanglement of two different thermal equilibrium states in zero and nonzero magnetic fields are obtained.
Based on a two-qubit isotropic Heisenberg XY model under a constant external magnetic field,we construct a four-level entangled quantum heat engine(QHE).The expressions for the heat transferred,the work,and the efficiency are derived.Moreover,the influence of the entanglement on the thermodynamic quantities is investigated analytically and numerically.Several interesting features of the variations of the heat transferred,the work,and the efficiency with the concurrences of the thermal entanglement of two different thermal equilibrium states in zero and nonzero magnetic fields are obtained.
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.
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.
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.
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.