Ramon van Handel and Hideo Mabuchi 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S226 doi:10.1088/1464-4266/7/10/005
Ramon van Handel and Hideo Mabuchi
Show affiliationsBoth in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by infinite dimensionality of the information state which severely limits its practical applicability, except in a few select cases (e.g. the linear Gaussian case). One solution proposed in classical filtering theory is that of the projection filter. In this scheme, the filter is constrained to evolve in a finite-dimensional family of densities through orthogonal projection on the tangent space with respect to the Fisher metric. Here we apply this approach to the simple but highly nonlinear quantum model of optical phase bistability of a strongly coupled two-level atom in an optical cavity. We observe near-optimal performance of the quantum projection filter, demonstrating the utility of such an approach.
42.50.Pq Cavity quantum electrodynamics; micromasers
42.79.Ci Filters, zone plates, and polarizers
03.65.Ta Foundations of quantum mechanics; measurement theory
42.65.Pc Optical bistability, multistability, and switching, including local field effects
Issue 10 (October 2005)
Received 13 March 2005, accepted for publication 29 April 2005
Published 14 September 2005
Ramon van Handel and Hideo Mabuchi 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S226
Ramon van Handel et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S179