Phase-controlled atom-photon entanglement in a three-level Λ -type closed-loop atomic system

We study the entanglement of dressed atom and its spontaneous emission in a three-level Λ -type closed-loop atomic system in multi-photon resonance condition and beyond it. It is shown that the von Neumann entropy in such a system is phase-dependent, and it can be controlled by either intensity or relative phase of applied fields. It is demonstrated that for the special case of Rabi frequency of applied fields, the system is disentangled. In addition, we take into account the effect of Doppler broadening on the entanglement and it is found that a suitable choice of laser propagation direction allows us to obtain the steady state degree of entanglement (DEM) even in the presence of Doppler effect.