Thermal entanglement of a V-type three-level atom and bimodal photons

Abstract

In this paper the properties of thermal entanglement between a V-type three-level atom and bimodal photons in an optical cavity is studied. The cavity is assumed to be in thermal equilibrium with a heat reservoir thus all atom–photon states with probabilities defined by Boltzmann factor are present. Introducing total atom–photon excitation operator (as conserved operator), it is shown that the Hamiltonian representation is block-diagonal each of dimensions 3N+1, where N is the eigenvalues of the total excitation operator. Each of these blocks consists of two 2 × 2 and N-1 3 × 3 irreducible subblocks. The thermal (Gibbs) density operator for the present system is then analytically calculated by diagonalizing the block matrices. The partially transposed density matrix with respect to the atomic states and consequently, the negativity, as a measure of entanglement, are determined as functions of temperature. The negativity shows that the system of the three-level atom and photons is separable at zero temperature, exhibits a maximum at a certain temperature and disentangles at a threshold finite temperature. Effect of atom–photon couplings and detunings (as controllable parameters) on thermal entanglement is also discussed in detail.