Non-Markovian quantum-state diffusion: Perturbation approach

We present a perturbation theory for non-Markovian quantum-state diffusion (QSD), the theory of diffusive quantum trajectories for open systems in a b osonic environment [Phys. Rev. A 58, 1699 (1998)]. We establish a systemati c expansion in the ratio between the environmental correlation time and the typical system time scale. The leading order recovers the Markov theory, s o here we concentrate on the next-order correction corresponding to first-o rder non-Markovian master equations. These perturbative equations greatly s implify the general non-Markovian QSD approach, and allow for efficient num erical simulations beyond the Markov approximation. Furthermore, we show th at each perturbative scheme for QSD naturally gives rise to a perturbative scheme for the master equation which we study in some detail. Analytical an d numerical examples are presented, including the quantum Brownian motion m odel.