Stability of various entanglements in the interaction between two two-level atoms with a quantized field under the influences of several decay sources

Abstract

In this paper the interaction between two two-level atoms with a single-mode quantized field is studied. To achieve exact information about the physical properties of the system, one should take into account various sources of dissipation such as photon leakage of cavity, spontaneous emission rate of atoms, internal thermal radiation of cavity and dipole–dipole interaction between the two atoms. In order to achieve the desired goals, we obtain the time evolution of the associated density operator by solving the time-dependent Lindblad equation corresponding to the system. Then, we evaluate the temporal behavior of total population inversion and quantum entanglement between the evolved subsystems, numerically. We clearly show that how the damping parameters affect on the dynamics of considered properties. By analyzing the numerical results, we observe that increasing each of the damping sources leads to faster decay of total population inversion. Also, it is observed that, after starting the interaction, the entanglement between one atom with other parts of the system as well as the entanglement between “atom–atom” subsystem and the “field”, tend to some constant values very soon. Moreover, the stable values of entanglement are reduced via increasing the damping factor $$\varGamma _{\mathrm{A}}$$ ( $$\varGamma _{\mathrm{A}}^{(1)} = \varGamma _{\mathrm{A}}^{(2)} = \varGamma _{\mathrm{A}}$$ ) where $$\varGamma _{\mathrm{A}}$$ is the spontaneous emission rate of each atom. In addition, we find that by increasing the thermal photons, the entropies (entanglements) tend sooner to some increased stable values. Accordingly, we study the atom–atom entanglement by evaluating the concurrence under the influence of dissipation sources, too. At last, the effects of dissipation sources on the genuine tripartite entanglement between the three subsystems include of two two-level atoms and a quantized field are numerically studied. Due to the important role of stationary entanglement in quantum information processing, our results may provide useful hints for practical protocols which require some appropriate mechanisms to prevent or at least minimize the influence of decoherence phenomenon.