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Acta Physica Sinica

A four-level quantum refrigeration cycle

He Xian, He Ji-Zhou, Xiao Yu-Ling

Published Jan 1, 2012• 4 citations
Publisher

Abstract

A four-level entangled quantum refrigeration cycle working with a two-qubit entangled system is proposed in this paper. Based on the first law of quantum thermodynamics and the concept of thermal entanglement, the relation between the quantum entanglement and the several thermodynamic quantities such as the heat transfer, the input work and the coefficient of performance is analyzed. It is found that the isoline of the coefficient of performance is the loop line and it no longer monotonically changes with the ratio of entanglement; in a small exchange constant J the operation region of the refrigerator is c1>c2 and in a larger exchange constant J the operation region of the refrigerator may be c1>c2 or c1c2; the maximal coefficient of performance increases as the exchange constant increases.

DOI
10.7498/aps.61.150302

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An entangled quantum refrigerator working with a two-qubit Heisenberg XX model in a constant external magnetic field is constructed in this paper. Based on the quantum first law of thermodynamics, the expressions for several basic thermodynamic quantities such as the heat transferred, the net work and the coefficient of performance are derived. Moreover, the influence of the thermal entanglement on the basic thermodynamic quantities is investigated. Several interesting features of the variation of the basic thermodynamic quantities with the thermal entanglement in zero and nonzero magnetic field are obtained. Lastly, we analyze the maximum coefficient of performance.
The four-level entangled quantum refrigerator (QR) is studied in the XXZ Heisenberg model for the two-qubits. The Hamiltonian of the problem includes the exchange parameters Jx = Jy = J and Jz = αJ along the x-, y- and z-directions, respectively, and constant external magnetic field B in the z-direction. The parameter α is introduced into the model which controls the strength of the exchange parameter Jz in comparison to Jx and Jy, thus, our investigation of QR includes the XX (α = 0.0), XXX (α = 1.0) and XXZ (for other α's) Heisenberg models. The two-qubits are assumed to be in contact with two heat reservoirs at different temperatures. The concurrences for a two-qubit are used as a measure of entanglement and then the expressions for the amount of heat transferred, the work performed and the efficiency are derived. The contour, i.e., the isoline maps, and some two-dimensional plots of the above mentioned thermodynamic quantities are illustrated.
An entangled quantum refrigerator working with a three-qubit one-dimensional isotropic Heisenberg XX model in a constant external magnetic field is constructed in this paper. Based on the quantum first law of thermodynamics, the expressions for several basic thermodynamic quantities such as the heat transferred, the net work and the coefficient of performance are derived. Moreover, the influence of the thermal entanglement on the basic thermodynamic quantities is investigated. Several interesting features of the variation of the basic thermodynamic quantities with the thermal entanglement in zero and nonzero magnetic field are obtained.
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.
An entangled quantum refrigerator working with a three-qubit one-dimensional isotropic Heisenberg XXmodel in a constant external magnetic field is constructed in this paper.Based on the quantum Erst law of thermodynamics,the expressions for several basic thermodynamic quantities such as the heat transferred,the net work and thecoefficient of performance are derived.Moreover,the influence of the thermal entanglement on the basic thermodynamicquantities is investigated.Several interesting features of the variation of the basic thermodynamic quantities with thethermal entanglement in zero and nonzero magnetic field are obtained.
Based on an isotropic two spin-1/2 qubits Heisenberg model with the Dzyaloshinskii—Moriya interaction in an external magnetic field, we have constructed an entangled quantum refrigerator. Expressions for the basic thermodynamic quantities, i.e., the heat exchanged, the net work input, and the coefficient of performance, are derived. Some intriguing features and their qualitative explanations in zero and non zero magnetic fields are given. The influence of the thermal entanglement on the refrigerator is investigated. The results obtained here have general significance and will be helpful to understand the performance of an entangled quantum refrigerator.