Characteristics of the Temporal Behavior of Entanglement between Photonic Binomial Distributions and a Two-Level Atom in a Damping Cavity

In the present study, temporal behavior of entanglement between photonic binomial distributions and a two-level atom in a leaky cavity, in equilibrium with the environment at a temperature T, is studied. In this regard, the master equation is solved in the secular approximation for the density matrix, when the initial photonic distribution is binomial, while the atomic states obey the Boltzmann distribution. The atom-photon density matrix so calculated is then used to compute the negativity, as a measure of entanglement. The behavior of atom-photon entanglement is, consequently, determined as a function of time and temperature. To justify the behavior of atom-photon entanglement, moreover, we employ the total density matrix to compute and analyze the time evolution of the initial photonic binomial probability distribution. Our results, along with representative figures reveal that the atom-photon degree of entanglement exhibits oscillations while decaying with time and asymptotically vanishes. It is further demonstrated that an increase in the temperature gives rise to a decrease in the entanglement. The finer characteristics of the temporal behavior of the corresponding probability distribution and, consequently, the atom-photon entanglement is also given and discussed.