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Adaptive single-shot phase measurements: The full quantum theory

Wiseman, H. M. and Killip, R. B. (1998) Adaptive single-shot phase measurements: The full quantum theory. Physical Review A, 57 (3). pp. 2169-2185. ISSN 1050-2947. doi:10.1103/PhysRevA.57.2169.

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The phase of a single-mode field can be measured in a single-shot measurement by interfering the field with an effectively classical local oscillator of known phase. The standard technique is to have the local oscillator detuned from the system (heterodyne detection) so that it is sometimes in phase and sometimes in quadrature with the system over the course of the measurement. This enables both quadratures of the system to be measured, from which the phase can be estimated. One of us [H. M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)] has shown recently that it is possible to make a much better estimate of the phase by using an adaptive technique in which a resonant local oscillator has its phase adjusted by a feedback loop during the single-shot measurement. In a previous work [H. M. Wiseman and R. B. Killip, Phys. Rev. A 56, 944 (1997)] we presented a semiclassical analysis of a particular adaptive scheme, which yielded asymptotic results for the phase variance of strong fields. In this paper we present an exact quantum mechanical treatment. This is necessary for calculating the phase variance for fields with small photon numbers, and also for considering figures of merit other than the phase variance. Our results show that an adaptive scheme is always superior to heterodyne detection as far as the variance is concerned. However, the tails of the probability distribution are surprisingly high for this adaptive measurement, so that it does not always result in a smaller probability of error in phase-based optical communication.

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Killip, R. B.0000-0002-4272-7916
Additional Information:©1998 The American Physical Society. Received 28 October 1997. H.M.W. would like to thank the Australian Research Council and R.B.K. the W.H. Pickering Foundation for financial support.
Issue or Number:3
Record Number:CaltechAUTHORS:WISpra98
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9443
Deposited By: Tony Diaz
Deposited On:02 Jan 2008
Last Modified:08 Nov 2021 20:59

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