Bayesian feedback control of a two-atom spin-state in an atom-cavity system.

We experimentally demonstrate real-time feedback control of the joint spin-state of two neutral cesium atoms inside a high finesse optical cavity. The quantum states are discriminated by their different cavity transmission levels. A Bayesian update formalism is used to estimate state occupation probabilities as well as transition rates. We stabilize the balanced two-atom mixed state, which is deterministically inaccessible, via feedback control and find very good agreement with Monte Carlo simulations. On average, the feedback loop achieves near optimal conditions by steering the system to the target state marginally exceeding the time to retrieve information about its state.