Stabilization of a delayed quantum system: the photon box case-study
Abstract
We study a feedback scheme to stabilize an arbitrary photon number state in a microwave cavity. The quantum non-demolition measurement of the cavity state allows a non-deterministic preparation of Fock states. Here, by the mean of a controlled field injection, we desire to make this preparation process deterministic. The system evolves through a discrete-time Markov process and we design the feedback law applying Lyapunov techniques. Also, in our feedback design we take into account an unavoidable pure delay and we compensate it by a stochastic version of a Smith predictor. After illustrating the efficiency of the proposed feedback law through simulations, we provide a rigorous proof of the global stability of the closed-loop system based 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.
Cite
@article{arxiv.1007.3584,
title = {Stabilization of a delayed quantum system: the photon box case-study},
author = {Hadis Amini and Mazyar Mirrahimi and Pierre Rouchon},
journal= {arXiv preprint arXiv:1007.3584},
year = {2010}
}
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