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.
Cite
@article{arxiv.1103.1724,
title = {Approximate stabilization of an infinite dimensional quantum stochastic system},
author = {Ram Somaraju and Mazyar Mirrahimi and Pierre Rouchon},
journal= {arXiv preprint arXiv:1103.1724},
year = {2015}
}
Comments
Submitted to CDC 2011