Forward-backward analysis of the photon-number evolution in a cavity

Abstract

A quantum system can be monitored through repeated interactions with meter systems. The state of the system at time $t$, represented by the density matrix $\ensuremath{\rho}(t)$, then becomes conditioned on the information obtained by the meters until that time. More insight in the state of the system at any time $t$ is provided, however, by taking into account the full detection of all meters interacting with the system both in the past and in the future of $t$. We present experiments that use near-resonant atomic probes to monitor the evolution of the quantized field in a cavity. The application of the forward-backward smoothing method to this quantum problem, justified by the past quantum state formalism [S. Gammelmark et al., Phys. Rev. Lett. 111, 160401 (2013)], allows us to resolve a posteriori dynamics, which is not reflected by the usual quantum state $\ensuremath{\rho}(t)$.