Thermal free entanglement of a Λ -type three-level atom and bimodal photons in an optical cavity

Quantum entanglement is usually affected by the temperature and surrounding environment, thus it has been observed at low temperatures. The creation and manipulation of entanglement at finite temperatures is of crucial interest. To fulfill creating robust free (distillable) entanglement at finite temperatures, in this article, thermally-induced free entanglement of a Λ-type three-level atom and bimodal photons amid an optical lossless cavity, is investigated. We assume that the system is in thermal equilibrium with an environment thus the probabilities for finding the system in either of its eigenvalues are associated with the Boltzmann distribution. Introducing a conserved (Casimir) operator, a standard and effective procedure is then developed to calculate analytically the eigenvalues and eigenstates of the Hamiltonian, and thereby, to compute the thermal density operator and its partial transpose over atomic states. To justify the behavior of free (distillable) atom–photon entanglement, the quantitative form of Peres–Horodecki criteria, i.e. the negativity, is calculated. The analytical calculations show that the negativity vanishes at zero temperature, approaches to its maximum at a specific temperature and subsequently decreases asymptotically to zero. Furthermore, it is also illustrated that the maximum is larger for stronger atom–photon coupling while it decreases for greater atom–photon detuning. In addition, it is deduced from the representative figures that how the atom–photon structure parameters influence on the negativity.