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

Authors: Hadis Amini, Mazyar Mirrahimi, Pierre Rouchon, IEEE Trans. Automatic Control, Vol. 57, no 8, pp. 1918 - 1930, Aug. 2012, DOI: 10.1109/TAC.2012.2195853
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.
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author = {Mazyar Mirrahimi, Hadis Amini, Pierre Rouchon},
title = {Stabilization of a Delayed Quantum System: The Photon Box Case-Study},
journal = {IEEE Trans. Automatic Control},
volume = {57},
number = {8},
pages = {1918 - 1930},
year = {2012},