Nonequilibrium thermal entanglement in three-qubit $XX$ model

TL;DR

This paper investigates how steady state entanglement in a three-qubit XX model is affected by temperature differences and coupling symmetry, revealing conditions for maximizing entanglement through bath temperature control.

Contribution

It introduces an effective Hamiltonian approach to analyze steady state entanglement in a three-qubit XX model coupled to thermal baths, highlighting the effects of symmetric and nonsymmetric couplings.

Findings

Symmetric couplings yield equal nearest-neighbor entanglement, maximized at equal bath temperatures.

Nonsymmetric couplings allow temperature differences to enhance entanglement.

Steady state entanglement can be controlled by adjusting bath temperatures.

Abstract

Making use of the master equation and effective Hamiltonian approach, we investigate the steady state entanglement in a three-qubit $XX$ model. Both symmetric and nonsymmetric qubit-qubit couplings are considered. The system (the three qubits) is coupled to two bosonic baths at different temperatures. We calculate the steady state by the effective Hamiltonian approach and discuss the dependence of the steady state entanglement on the temperatures and couplings. The results show that for symmetric qubit-qubit couplings, the entanglements between the nearest neighbor are equal, independent of the temperatures of the two baths. The maximum of the entanglement arrives at $T_L=T_R$. For nonsymmetric qubit-qubit couplings, however, the situation is totally different. The baths at different temperatures would benefit the entanglement and the entanglements between the nearest neighbors are no longer equal. By examining the probability distribution of each eigenstate in the steady state, we present an explanation for these observations. These results suggest that the steady entanglement can be controlled by the temperature of the two baths.