Quantum Trajectories for Realistic Photodetection II: Application and Analysis

In the preceding paper [Warszawski and Wiseman] we presented a general formalism for determining the state of a quantum system conditional on the output of a realistic detector, including effects such as a finite bandwidth and electronic noise. We applied this theory to two sorts of photodetectors: avalanche photodiodes and photoreceivers. In this paper we present simulations of these realistic quantum trajectories for a cavity QED scenario in order to ascertain how the conditioned state varies from that obtained with perfect detection. Large differences are found, and this is manifest in the average of the conditional purity. Simulation also allows us to comprehensively investigate how the quality of the the photoreceiver depends upon its physical parameters. In particular, we present evidence that in the limit of small electronic noise, the photoreceiver quality can be characterized by an {\em effective} bandwidth, which depends upon the level of electronic noise and the filter bandwidth. We establish this result as an appropriate limit for a simpler, analytically solvable, system. We expect this to be a general result in other applications of our theory.