Quasi-probability distribution functions for a single trapped ion interacting with a mixed laser field

We give a fully analytical description of the dynamics of the quasi-probability distribution (Q-PD) functions for any model describing a single two-level qubit interacting with a field. The Wigner function at time (t = 0) and Q function for a pure state as an initial field state are studied. But, in this paper, the temporal behavior of the Q-PD functions for a coherent superposition state (SS) and a statistical mixture of coherent states (SM) for the interaction between a single ion and laser field are investigated. It is found that, the temporal behavior of the Q-PD functions is in very good agreement with its counterpart for the entanglement. If the curve of the entanglement between the trapped ion (specially for the second red sideband) and laser field are known, we can expect the shape of the Q-PD functions.