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Continuous measurement of canonical observables and limit stochastic Schrödinger equations

Continuous measurement of canonical observables and limit stochastic Schrödinger equations We derive the stochastic Schrödinger equation for the limit of continuous weak measurement where the observables monitored are canonical position and momentum. To this end we extend an argument due to Smolianov and Truman from the von Neumann model of indirect measurement of position to the Arthurs and Kelly model for simultaneous measurement of position and momentum. We require only unbiasedness of the detector states and an integrability condition sufficient to ensure a central limit effect. Despite taking a weak interaction as opposed to a weak measurement limit, the resulting stochastic wave equation is of the same form as that derived in a recent paper by Scott and Milburn for the specific case of joint Gaussian states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Continuous measurement of canonical observables and limit stochastic Schrödinger equations

Physical Review A , Volume 69 (3) – Mar 1, 2004
7 pages

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References (15)

Publisher
American Physical Society (APS)
Copyright
Copyright © 2004 The American Physical Society
ISSN
1094-1622
DOI
10.1103/PhysRevA.69.032107
Publisher site
See Article on Publisher Site

Abstract

We derive the stochastic Schrödinger equation for the limit of continuous weak measurement where the observables monitored are canonical position and momentum. To this end we extend an argument due to Smolianov and Truman from the von Neumann model of indirect measurement of position to the Arthurs and Kelly model for simultaneous measurement of position and momentum. We require only unbiasedness of the detector states and an integrability condition sufficient to ensure a central limit effect. Despite taking a weak interaction as opposed to a weak measurement limit, the resulting stochastic wave equation is of the same form as that derived in a recent paper by Scott and Milburn for the specific case of joint Gaussian states.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Mar 1, 2004

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