Stabilization of cavity Hilbert subspaces in cavity quantum electrodynamics by measurement-based quantum feedback*

Measurement-based quantum feedback (MBQFB) for actively preparing and stabilizing Fock number states in a cavity quantum electrodynamics (CQED) set-up has been achieved by Haroche et al. The approach relies on injecting, after each weak dispersive measurement of the cavity state using Rydberg atoms flying through the cavity as sensors, a low average photon number classical coherent field to steer the cavity towards the targeted number state. Preparing and stabilizing a superposition of Fock states using MBQFB is more challenging since the superposition must be an eigenstate of the quantum measurement operators. This condition requires that each Fock state composing the superposition be an eigenstate with the same eigenvalue for each measurement operator. Owing to the special form of the measurement operators in the dispersive regime, this constrains the phase shift per photon to specific values and leads to the stabilization of subspaces. Results from realistic simulations taking into account decoherence and imperfections in a CQED set-up will be presented. These support the validity of the underlying theory that generalizes the previous theory for preparing Fock number states.