Dynamical Properties of Scaled Atomic Wehrl Entropy of Multiphoton JCM in the Presence of Atomic Damping

We study the dynamics of the atomic inversion, scaled atomic Wehrl entropy, and marginal atomic Q-function for a single two-level atom interacting with a one-mode cavity field taking in the presence of atomic damping. We obtain the exact solution of the master equation in the interaction picture using specific initial conditions. We examine the effects of atomic damping parameter and number of multiphoton transition on the scaled atomic Wehrl entropy, atomic Q-function, and their marginal distribution. We observe an interesting monotonic relation between the different physical quantities in the case of different values of the number of photon transition during the time evolution. 1. Introduction Entanglement is a property of correlations between two or more quantum systems [1]. These correlations defy classical description and are associated with intrinsically quantum phenomena. This nonlocal nature of entanglement has also been identified as an essential resource for many novel tasks such as quantum computation, quantum teleportation [2], superdense coding [3], quantum cryptography [4, 5], and more recently, one-way quantum computation [6], and quantum metrology [7]. These quantum information tasks cannot be carried out by classical resources and they rely on entangled states. This recognition led to an intensive search for mathematical tools that would enable a proper quantification of this resource [8]. In particular, it is of primary importance to test whether a given quantum state is separable or entangled. It is well known that the Jaynes-Cummings model (JCM) becomes more a realistic and experimental model under the effect of damping [9]. Besides the experimental drive, also there exists a theoretical motivation to include relevant damping mechanism to the JC model because its dynamics becomes more interesting. In this regard, many authors have treated the JCM with dissipation by the use of analytic approximations [10, 11] and numerical calculations [12–14]. The solution in the presence of dissipation is not only of theoretical interest but also important from a practical point of view since dissipation would be always present in any experimental realization of the model. However, the dissipation treated in the above studies is modeled by coupling to an external reservoir including energy dissipation. As is well known, in a dissipative quantum system, the system loses energy by creating a bath quantum. Over the last two decades, much attention has been focused on information entropies as a measure of the entanglement in quantum information [1]. In