Narrow Results

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 J_x = J_y = J and J_z = 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 J_z in comparison to J_x and J_y, 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.

Brunner et al. [Phys. Rev. E 85 (2012) 05111] have claimed that, "essentially only the smallest machines can approach Carnot efficiency". We have verified this claim by raising self-contained four-qubit quantum refrigerator, and we have shown that according to concepts of virtual qubit, it can reach the maximum efficiency in other words Carnot efficiency. But its efficiency, such as self-contained three-qubit quantum refrigerator is not universal. We also investigated a special case of self-contained four-qubit quantum refrigerator, in other words self-contained four-qubit quantum refrigerator with two hot baths in the same temperature. We demonstrated that its efficiency has the form as efficiency of a self-contained three-qubit quantum refrigerator. In other words, from the perspective of efficiency, this particular model is equivalent to self-contained three-qubit quantum refrigerator. We also demonstrated the efficiency of this particular model in the Carnot limit that is independent from details of system model, but only depends on the environmental temperatures. Also, we raised a system that consists of n-qubit which acts as a refrigerator. According to self-contained four-qubit quantum refrigerator, we also investigated a special case of self-contained n-qubit quantum refrigerator — a self-contained n-qubit quantum refrigerator with (n - 2) baths in the same temperature. We considered the three different special situations of the n-qubit refrigerator and demonstrated their efficiency in three different situations which has the form as efficiency of self-contained three-qubit quantum refrigerator. In this special situations, (n - 2) qubits are in thermal contact with isothermal heat baths.

We study the effects of common reservoirs on the performance of an autonomous three-level quantum refrigerator. We show that the common reservoirs can result not only in additional transitions but also different types of interferences between them. For the case that the sole object to be cooled is a cold reservoir, it turns out that the cooling power can be greatly enhanced by the common reservoirs as well as by the induced interference. For the configuration that the refrigerator acts on both the cold reservoir and a qubit, we find that though the common reservoirs can improve the cooling power, which instead is detrimental to the cooling of the qubit. The interference also manifests different effects on the cooling of the cold reservoir and the qubit. Our results provide an evidence of possibility on applying the common reservoirs to enhance the performance of the refrigerator.