Stabilization of a Delayed Quantum System: The Photon Box Case-Study

Hadis Amini (1) , Mazyar Mirrahimi (2) , Pierre Rouchon (1)

1 CAS - Centre Automatique et Systèmes
2 SISYPHE - SIgnals and SYstems in PHysiology & Engineering

A feedback scheme, stabilizing an arbitrary photon-number state in a microwave cavity, is analyzed. The quantum non-demolition measurement of the cavity state allows in open-loop a non-deterministic preparation of photon-number states. By the mean of a controlled classical field injection, this preparation process is made deterministic. The system evolves through a discrete-time Markov process and the feedback law relies on Lyapunov techniques. This feedback design compensates an unavoidable pure delay by a stochastic version of a Kalman-type predictor. After illustrating the efficiency of the proposed feedback law through simulations, the global closed-loop convergence is proved. It relies on tools from stochastic stability analysis. A brief study of the Lyapunov exponents of the linearized system around the target state gives a strong indication of the robustness of the method.

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

Hadis Amini, Mazyar Mirrahimi, Pierre Rouchon. Stabilization of a Delayed Quantum System: The Photon Box Case-Study. IEEE Transactions on Automatic Control, 2012, 57 (8), pp.1918 - 1930. ⟨10.1109/TAC.2012.2195853⟩. ⟨hal-00755188⟩