Continuous measurement and non-Markovian quantum trajectories

Based on a microscopic model of an open system consisting of a boson field coupled linearly to a system, we formulate quantum trajectories as continuous measurements of the output field from the system. We present a formulation for the case when the field quantity that is being monitored effectively commutes with itself at different times. In general, this results in a non-Markovian evolution for the reduced system conditioned on the measurements. Under the finite-memory time approximation this evolution can be numerically simulated. The generalization of the techniques of quantum trajectories to the non-Markovian regime is expected to contribute to our understanding of open system problems beyond the Born-Markov approximation.