Thermal atom–atom entanglement in a nonlinear cavity

Abstract

In the present report thermal entanglement between two-coupled two-level atoms as two identical qubits inside a single mode lossless cavity, filled with a centrosymmetric medium, is investigated. In the presence of the centrosymmetric medium, photonic cavity mode couples with itself via the third order susceptibility. The cavity is also assumed to be in thermal equilibrium with a heat reservoir so that all atom–photon states with definite probabilities participate into the entanglement. A Casimir operator of the system, which commutes with the total Hamiltonian, indicates that the Hamiltonian representation is block-diagonal. Diagonalizing of each block, the thermal density operator, written in the bases of total Hamiltonian, is obtained. Partial tracing of thermal density matrix over the photonic states, the atomic reduced density matrix, and consequently, the concurrence, as a measure of entanglement, are determined as functions of temperature. The concurrence shows that the thermal atom–atom entanglement starts from zero at zero temperature, becomes more entangled, reaching the maximal at a critical temperature and terminates abruptly at a finite temperature. The influence of medium on the thermal atom–atom entanglement is also examined.