Wigner-function Evolution and Photon-number Decay of Quantum States in a Laser Cavity with the Kerr Medium

Using the thermal-entangled state representation theory, we solve the master equation describing a laser cavity with the Kerr medium, and find that the analytical evolution law of the density operator is governed by the infinitive Kraus operator-sum representation. Also, we obtain a new evolution formula of the Wigner function (WF) for any initial state in this cavity by rewriting the WF as a scalar product between two pure states. In term of the new WF formula, the WF evolution of the initial coherent and number states and the decay of photon number are also presented.