Stabilization of photon-number states via single-photon corrections: A convergence analysis under imperfect measurements and feedback delays

This paper presents a 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 the Laboratoire Kastler Brossel. Here, we consider an infinite-dimensional Markov model corresponding to a realistic experimental set-up where imperfect measurements and feedback delays are taken into account. In this realistic 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 subspace. Closed-loop simulations illustrate the performance of the feedback law.