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Approximate stabilization of an infinite dimensional quantum stochastic system

Abstract : We propose a feedback scheme for preparation of photon number states in a microwave cavity. Quantum Non-Demolition (QND) measurements of the cavity field and a control signal consisting of a microwave pulse injected into the cavity are used to drive the system towards a desired target photon number state. Unlike previous work, we do not use the Galerkin approximation of truncating the infinite-dimensional system Hilbert space into a finite-dimensional subspace. We use an (unbounded) strict Lyapunov function and prove that a feedback scheme that minimizes the expectation value of the Lyapunov function at each time step stabilizes the system at the desired photon number state with (a pre-specified) arbitrarily high probability. Simulations of this scheme demonstrate that we improve the performance of the controller by reducing "leakage" to high photon numbers.
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Contributor : François Chaplais <>
Submitted on : Wednesday, March 28, 2012 - 5:15:24 PM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM
Long-term archiving on: : Friday, June 29, 2012 - 2:27:32 AM

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Ram Somaraju, Mazyar Mirrahimi, Pierre Rouchon. Approximate stabilization of an infinite dimensional quantum stochastic system. CDC-ECC 2011 : 50th IEEE Conference on Decision and Control and European Control Conference, Dec 2011, Orlando, United States. pp.6248 - 6253, ⟨10.1109/CDC.2011.6160560⟩. ⟨hal-00683444⟩

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