Stationary phase-space information in a qubit interacting non-linearly with a lossy single-mode field in the off-resonant case

An analytical description of a qubit interacting non-linearly and non-resonantly with a lossy cavity via intensity-dependent coupling has been obtained. With the amplitude cavity damping as a particular type of the thermal amplitude reservoir damping, Wehrl entropy and Wehrl density are used to investigate the dynamics of the loss of both qubit coherence and information. We show that the Q-function Wehrl entropy and its density are very sensitive not only to the amplitude cavity damping and the intensity of the coherent state but also to the frequency detuning. The information of the phase space and the coherence are quickly lost due to the coupling to the environment. When the qubit interacting non-linearly with the lossy cavity, we observe: (1) The mixedness of the atomic state can be decreased by increasing the coupling to the environment. (2) For the off-resonance case, if the cavity damping is increased, the information of the mixed evolved state can be protected.