Entanglement between atomic thermal states and coherent or squeezed photons in a damping cavity

In the present study, the standard Jaynes–Cummings model, in a lossy cavity, is employed to characterize the entanglement between atoms and photons when the former is initially in a thermal state (mixed ensemble) while the latter is described by either coherent or squeezed distributions. The whole system is thus assumed to be in equilibrium with a heat reservoir at a finite temperature T, and the measure of negativity is used to determine the time evolution of atom–photon entanglement. To this end, the master equation for the density matrix, in the secular approximation, is solved and a partial transposition of the result is made. The degree of atom–photon entanglement is then numerically computed, through the negativity, as a function of time and temperature. To justify the behavior of atom–photon entanglement, moreover, we employ the so obtained total density matrix to compute and analyze the time evolution of the initial photonic coherent or squeezed probability distributions and the squeezing parameters. On more practical points, our results demonstrate that as the initial photon mean number increases, the atom–photon entanglement decays at a faster pace for the coherent distribution compared to the squeezed one. Moreover, it is shown that the degree of atom–photon entanglement is much higher and more stable for the squeezed distribution than that for the coherent one. Consequently, we conclude that the time intervals during which the atom–photon entanglement is distillable is longer for the squeezed distribution. It is also illustrated that as the temperature increases the rate of approaching separability is faster for the coherent initial distribution. The novel point of the present report is the calculation of dynamical density matrix (containing all physical information) for the combined system of atom–photon in a lossy cavity, as well as the corresponding negativity, at a finite temperature.