Non-Markovian quantum trajectories for spectral detection

We present a formulation of non-Markovian quantum trajectories for open sys tems from a measurement theory perspective. In our treatment there are thre e distinct ways in which non-Markovian behavior can arise: a mode-dependent coupling between the hath (reservoir) and system, a dispersive bath, and s pectral detection of the output into the bath. In the first two cases the n on-Markovian behavior is intrinsic to the interaction; in the third case th e non-Markovian behavior arises from the method of detection. We focus in d etail on the trajectories that simulate real-time spectral detection of the light emitted from a localized system. In this case the non-Markovian beha vior arises from the uncertainty in the time of emission of particles that are later detected. The results of computer simulations of the spectral det ection of the spontaneous emission from a strongly driven two-level atom ar e presented. [S1050-2947(99)01403-1].