WIGNER DISTRIBUTION FUNCTION OF A SIMPLE OPTICAL-SYSTEM - AN EXTENDED-PHASE-SPACE APPROACH

We construct the Wigner distribution function for a coupled boson-fermion system. This function is regarded as a certain "superfield" defined on the extended phase space, the points of which are labeled by the anticommuting canonical c variables together with the ordinary ones. In this approach, the variables of a fermion and a boson are treated on a completely equal footing, and the phase-space representation is fully realized. We apply the formalism to the kinetic theory of the optical Dicke model with a two-level atom, and show how systematically a set of the generalized Fokker-Planck equations, which describes the effective dynamics of the radiation field, is derived from a single superfieldlike equation.