Quantum trajectories for realistic photodetection: II. Application and analysis

Abstract

In the preceding paper (Warszawski P and Wiseman H M 2002 J. Opt. B: Quantum Semiclass. Opt. 4 1) 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 photodetector: avalanche photodiodes and photoreceivers. In this paper we present simulations of these realistic quantum trajectories for a cavity quantum electro-dynamics 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 photoreceiver (PR) depends upon its physical parameters. In particular, we present evidence that in the limit of small electronic noise, the PR quality can be characterized by an 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.