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Quantum projection filter for a highly nonlinear model in cavity QED

van Handel, Ramon and Mabuchi, Hideo (2005) Quantum projection filter for a highly nonlinear model in cavity QED. Journal of Optics B: Quantum and Semiclassical Optics, 7 (10). S226-S236. ISSN 1464-4266. http://resolver.caltech.edu/CaltechAUTHORS:HANjob05a

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Abstract

Both 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.


Item Type:Article
Additional Information:Copyright © 2005 Institute of Physics Received 13 March 2005, accepted for publication 29 April 2005, Published 14 September 2005, Print publication: Issue 10 (October 2005) The authors thank Mike Armen for useful discussions. This work was supported by the ARO (DAAD19-03-1-0073).
Subject Keywords:quantum filtering, model reduction, Fisher metric, Wonham filter
Record Number:CaltechAUTHORS:HANjob05a
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:HANjob05a
Alternative URL:http://dx.doi.org/10.1088/1464-4266/7/10/005
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1872
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:21 Feb 2006
Last Modified:26 Dec 2012 08:46

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