Wiener–Hermite expansion formalism for the stochastic model of a driven quantum system Original Research Article

The time evolution of a simple two-level system with a periodic modulation of the energy levels superimposed with a stochastic fluctuation is investigated. The Wiener–Hermite expansion method is successfully applied to the numerical solution of the equation of motion. In this method, we transform the stochastic equation into an infinite set of simultaneous deterministic equations, which can be solved by truncating it into a finite one. Two types of mechanisms of phase relaxation are exhibited to modify the population dynamics. The one is the homogeneous phase relaxation in the rapid fluctuation limit, and the other is the inhomogeneous phase relaxation in the slow fluctuation limit.