  Quantum trajectories describe the stochastic evolution of an open quantum
system conditioned on continuous monitoring of its output, such as by an ideal
photodetector. Here we derive (non-Markovian) quantum trajectories for
realistic photodetection, including the effects of efficiency, dead time,
bandwidth, electronic noise, and dark counts. We apply our theory to a
realistic cavity QED scenario and investigate the impact of such detector
imperfections on the conditional evolution of the system state. A practical
theory of quantum trajectories with realistic detection will be essential for
experimental and technological applications of quantum feedback in many areas.
