Non-Markovian open quantum systems: Input-output fields, memory, and monitoring

Principles of monitoring non-Markovian open quantum systems are analyzed. We use a field representation of the environment [C. W. Gardiner and M. J. Collett, Phys. Rev. A 31, 3761 (1985)] for the separation of its memory and detector part, respectively. We claim that the system-plus-memory compound becomes Markovian; the detector part is tractable by standard Markovian monitoring. Because of non-Markovianity, only the mixed state of the system can be predicted; the pure state of the system can be retrodicted. We present the corresponding non-Markovian stochastic Schrodinger equation.