  This paper presents a first mathematical convergence analysis of a Fock
states feedback stabilization scheme via single-photon corrections. This
measurement-based feedback has been developed and experimentally tested in 2012
by the cavity quantum electrodynamics group of Serge Haroche and Jean-Michel
Raimond. Here, we consider the infinite-dimensional Markov model corresponding
to the ideal set-up where detection errors and feedback delays have been
disregarded. In this ideal context, we show that any goal Fock state can be
stabilized by a Lyapunov-based feedback for any initial quantum state belonging
to the dense subset of finite rank density operators with support in a finite
photon-number sub-space. Closed-loop simulations illustrate the performance of
the feedback law.
