Quantum trajectories and quantum control: Theory and cavity-QED experiment

Quantum trajectories describe the stochastic evolution of an open quantum system conditioned on continuous monitoring of its output, such as by an ideal photodetector. They are useful for answering questions of principle, for conditional state preparation, and (probably most importantly) for quantum feedback control systems. For the latter two applications, it is necessary to use quantum trajectories for realistic detectors, and we outline a theory to do this. Finally, we present the first experimental results for quantum feedback in the "deep quantum" regime where quantum trajectories must be used for designing and modeling the feedback. In a cavity QED system we show that a state conditioned on the detection of a single photon can be frozen (its dynamics stopped) and then released after an arbitrary lapse of time.