Statistical Aspects and Dynamical Entanglement for a Two-Level Atom Moving on Along Cavity Length of x-Direction: Atomic Position Distribution

Abstract

In this work, the problem of the quantum optical model is considered where an one-mode quantized radiation field interacts with a two-level atom (TLA). Also, the atomic position distribution is taken into account, i.e., the atom passing through the length of the optical cavity. We believe that the atomic position affects the matter-field interaction and can be realized in several multiple experiments, such as ultracold atoms and trapped ions. We take into consideration the atom is moving along the cavity field in the x-direction so that the time-position Schrödinger equation for the atom in the x-direction is obtained. We suppose that the field is initially prepared in a coherent state optical field and the atom is initially prepared in an excited state. Also, the atomic motion along the cavity length vanishes in the cavity wall. By using the Laplace transformation method, an exact analytical solution for the coupled partial differential Schrödinger equation for the wave function is calculated. Some non-classical statistical aspects such as the atomic inversion and the photon distributions are discussed in detail. The collapses-revivals, the Poissonian distributions of the photon by Mandel Q parameter, the degrees of the entanglement, and the fidelity have been investigated. The effect of the atomic position distribution in the x-direction on these phenomena is examined. We observed that the atomic position distribution along the cavity has an effective effect on the quantum statistical properties of these phenomena. Minutely, the influence of the atom location distribution on the amount of quantum entanglement has been obtained.