We analyze the quantum jumps of an atom interacting with a cavity field, where strong coupling makes the cavity transmission depend on the time-dependent atomic state. In our analysis we employ a Bayesian approach that conditions the population of the atomic states at time t on the cavity transmission observed both before and after t, and we show that the state assignment by this approach is more decisive than the usual conditional quantum states based on only earlier measurement data. We also provide an iterative protocol which, together with the atomic state populations, simultaneously estimates the atomic jump rates and the transmission signal distributions from the measurement data. Finally, we take into account technical fluctuations in the observed signal, e.g., due to spatial motion of the atom within the cavity, by representing atomic states by several hidden states, thereby significantly improving the state's recovery.

}, Author = {Gammelmark, S. AND Alt, W. AND Kampschulte, T. AND Meschede, D. AND Mølmer, K.}, Journal = {Phys. Rev. A}, Pages = {043839}, Title = {{Hidden Markov Model of atomic quantum jump dynamics in an optically probed cavity}}, Volume = {89}, Year = {2014} }