Quantum feedback by discrete quantum non-demolition measurements: towards on-demand generation of photon-number states

We propose a quantum feedback scheme for the preparation and protection of photon number states of light trapped in a high-Q microwave cavity. A quantum non-demolition measurement of the cavity field provides information on the photon number distribution. The feedback loop is closed by injecting into the cavity a coherent pulse adjusted to increase the probability of the target photon number. The efficiency and reliability of the closed-loop state stabilization is assessed by quantum Monte-Carlo simulations. We show that, in realistic experimental conditions, Fock states are efficiently produced and protected against decoherence.