A feedback scheme for preparation of photon number states in a microwave
cavity is proposed. Quantum Non Demolition (QND) measurement of the cavity
field provides information on its actual state. The control consists in
injecting into the cavity mode a microwave pulse adjusted to maximize the
population of the desired target photon number. In the ideal case (perfect
cavity and measures), we present the feedback scheme and its detailed
convergence proof through stochastic Lyapunov techniques based on
super-martingales and other probabilistic arguments. Quantum Monte-Carlo
simulations performed with experimental parameters illustrate convergence and
robustness of such feedback scheme.Comment: submitted, update version with feedback law of arXiv:0905.0114
[quant-ph