Optomechanical cavities are one of the most important systems for observing quantum phenomena. In this paper, we investigated the quantum aspect of an optomechanical system made up of a two-level atom under two laser pump stimulation. One of the laser pumps drives the optical cavity, known as a longitudinal pump, while the second laser was used to excite the atom inside the cavity, directly and called as transverse pump. We observe the quasi-random walk of atom inside the cavity. Next, entanglement evolution among the atomic states and the other parts of the system with the von Neumann entropy measure was investigated. The study was done for distinctive atomic states in a strong coupling regime between the atom and field of cavity. Also, we investigated the evidence for non-Markovian behavior with trace distance measure. Our results demonstrate that the random walk of the atom can offer assistance to us to upgrade the entanglement between the inside atom mode and the other parts of the system for a long time. Furthermore, adding atomic motion provides evidence for the non-Markovian treatment of the system at the initial time

Keywords