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Stabilization of photon-number states via single-photon corrections: a first convergence analysis under an ideal set-up

Authors: Hector Bessa Silveira, Paulo Sergio Pereira da Silva, Pierre Rouchon, CDC 2015, Dec 15-18 2015, Osaka
This paper presents a first mathematical convergence analysis of a Fock states feedback stabilization scheme via single-photon corrections. This measurement-based feedback has been developed and experimentally tested in 2012 by the cavity quantum electrodynamics group of Serge Haroche and Jean-Michel Raimond. Here, we consider the infinite-dimensional Markov model corresponding to the ideal set-up where detection errors and feedback delays have been disregarded. In this ideal context, we show that any goal Fock state can be stabilized by a Lyapunov-based feedback for any initial quantum state belonging to the dense subset of finite rank density operators with support in a finite photon-number sub-space. Closed-loop simulations illustrate the performance of the feedback law.
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BibTeX:
@Proceedings{2015-12-16,
author = {Hector Bessa Silveira, Paulo Sergio Pereira da Silva, Pierre Rouchon},
editor = {},
title = {Stabilization of photon-number states via single-photon corrections: a first convergence analysis under an ideal set-up},
booktitle = {CDC 2015},
volume = {},
publisher = {},
address = {},
pages = {},
year = {2015},
abstract = {This paper presents a first mathematical convergence analysis of a Fock states feedback stabilization scheme via single-photon corrections. This measurement-based feedback has been developed and experimentally tested in 2012 by the cavity quantum electrodynamics group of Serge Haroche and Jean-Michel Raimond. Here, we consider the infinite-dimensional Markov model corresponding to the ideal set-up where detection errors and feedback delays have been disregarded. In this ideal context, we show that any goal Fock state can be stabilized by a Lyapunov-based feedback for any initial quantum state belonging to the dense subset of finite rank density operators with support in a finite photon-number sub-space. Closed-loop simulations illustrate the performance of the feedback law.},
keywords = {}}