Microscopic Theory of Laser Master Equation up to the Forth Order

Miguel Orszag

Miguel Orszag

Miguel Orszag

Toshihico Arimitsu, Tetsuo Tominaga

A laser master equation is derived microscopically by using the time-convolution-less formulation of the damping theory up to the fourth-order terms with respect to the coupling constant between the laser field and the atoms, in order to investigate the quantum effect and the system size (number of the active atoms) dependence of the kinetic operator . The master equation is compared with the equation given by the time-convolution formalism which is essentially equal to the master equation derived by Haake.

Adi R. Bulsara, William C. Schieve

We consider the problem of two-photon transitions between atomic levels having the same parity. The semiclassical theory is developed from Maxwell's equations and the resulting transcendental equations for the pulse envelope solved exactly. They lead to an unstable pulse envelope if the higher-order processes are included. We then treat the laser as a birth/death process, deriving a Markovian (macroscopic) master equation for the probability function, which may be solved exactly in the steady state. By a suitable truncation procedure, this equation predicts a stable steady-state envelope, and is consistent with the microscopic quantum theory when virtual processes are neglected. A comparison is made between the macroscopic (master equation) approach and the microscopic quantum theory at the level of the moment equations. We find that, in the high-gain limit, the fluctuations predicted by the two theories are the same.