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arXiv · 1503.06933

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

Hector Bessa Silveira·Paulo Sergio Pereira da Silva·Pierre Rouchon
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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.

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Hector Bessa Silveira, Paulo Sergio Pereira da Silva, Pierre Rouchon. 2015-03-24. Stabilization of photon-number states via single-photon corrections: a first convergence analysis under an ideal set-up. https://doi.org/10.1109/cdc.2015.7403341

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