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

TL;DR

This paper provides the first mathematical convergence analysis of a feedback scheme for stabilizing photon-number states using single-photon corrections, assuming an ideal measurement setup without errors or delays.

Contribution

It introduces a Lyapunov-based feedback stabilization method for Fock states and proves its convergence in an idealized infinite-dimensional quantum system.

Findings

Any Fock state can be stabilized from finite-rank initial states.

The feedback law converges in the ideal measurement model.

Simulations demonstrate the effectiveness of the stabilization approach.

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.