Preparation and Stabilisation of a Non-Classical Field in Cavity by Quantum Feedback

Feedback loops are central to most classical control procedures. A controller compares the signal measured by a sensor with the target value or set-point. It then adjusts an actuator to stabilize the signal around the target value. Generalizing this scheme to the quantum world must overcome a fundamental difficulty: the sensor measurement cause a random back-action on the system. In this manuscript, we demonstrate the first continuously operated quantum feedback loop. The system to be controlled is a mode of the electromagnetic field trapped in a very high finesse microwave Fabry-Perot cavity. Circular Rydberg atoms achieve a quantum non-demolition measurement of the photon number in the mode by the succession of weak measurements. Knowing the outcome of these measurements, and knowing all the experimental imperfections of the system, a classical computer estimates in real-time the density matrix of the field. It then calculates the amplitude of small classical microwave fields injected into the cavity in order to stabilize the field around a target state. In this thesis, we have been able to prepare on demand and stabilize Fock states containing from 1 to 4 photons. (author)