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

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 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 rho(t).