We analyze the quantum jumps of an atom interacting with a cavity field. The strong atom- field interaction makes the cavity transmission depend on the time dependent atomic state, and we present a Hidden Markov Model description of the atomic state
dynamics which is conditioned in a Bayesian manner on the detected signal. We suggest that small variations in the observed signal may be due to spatial motion of the atom within the cavity, and we represent the atomic system by a number of hidden states to account for both the small variations and the internal state jump dynamics. In our theory, the atomic state is determined in a Bayesian manner from the measurement data, and we present an iterative protocol, which determines both the atomic state and the model parameters. As a new element in the treatment of observed quantum systems, we employ a Bayesian approach that conditions the atomic state at time t on the data acquired 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.
