Investigation of the time evolution of entanglement and trace distance in an atom-cavity system described with random walk and non-random walk states

An atom-cavity system consists of an atom or group of atoms inside a cavity. When an atom in cavity is stimulated by a laser pump, it is affected by the atom-field interaction shows the quasi-random walk behavior. This can change the entanglement and trace distance of system. In this work, the change entanglement and trace distance of system in two different cases namely the random walk and non-random walk is considered. The descriptive system is a two-level atom in the electrodynamics cavity based on the Jaynes-Cummings model, which is stimulated by two longitudinal and transverse laser pumps. The results show that the consideration of the random walk case for the atom changes in the amount of entanglement can be seen as the phenomenon of sudden death and birth of entanglement. It results in its rate of changes to be increased. In contrast to the non-random walk case, this rate is increased and decreased more quickly compared to the random walk case. The maximum amount of entanglement in each case is the same, but the minimum in random walk case is less than that of non-random walk case.