Dynamical evolution of photon-added thermal state in thermal reservoir

The dynamical behavior of a photon-added thermal state (PATS) in a thermal reservoir is investigated by virtue of Wigner function (WF) and Wigner logarithmic negativity (WLN), where this propagation model is abstracted as an input-output problem in a thermal-loss channel. The density operator of the output optical field at arbitrary time can be expressed in the integration form of the characteristics function of the input optical field. The exact analytical expression of WF is given, which is closely related to the Laguerre polynomial and is dependent on the evolution time and other interaction parameters (related with the initial field and the reservoir). Based on the WLN, we observe the dynamical evolution of the PATS in the thermal reservoir. It is shown that the thermal noise will make the PATS lose the non-Gaussianity.