Evolution of Coherent Light in a Simple Polariton Model

We study the phase evolution behaviour of coherent light interacting with phonons initially in thermal equilibrium at temperature T in terms of phase distribution probability. It is shown that the phase not only shifts but also diffuses. The phase distribution broadens and narrows periodically with time. There is a threshold in the variation of the width of phase distribution as a function of coupling coefficient in the detuning case for fixed temperature. The phase diffusion changes rapidly with temperature for coupling coefficient
above the threshold while it changes little with temperature for coupling coefficient below the threshold.