Stabilization of a Delayed Quantum System: The Photon Box Case-StudyReport as inadecuate




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

Abstract : 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.





Author: Hadis Amini - Mazyar Mirrahimi - Pierre Rouchon -

Source: https://hal.archives-ouvertes.fr/



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