dorsal/arxiv
View SchemaAdaptive single-shot phase measurements: The full quantum theory
| Authors | H. M. Wiseman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9710056 |
| URL | https://arxiv.org/abs/quant-ph/9710056 |
| DOI | 10.1103/PhysRevA.57.2169 |
Abstract
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 Ref.~[H.M. Wiseman and R.B. Killip, Phys. Rev. A 56, 944] 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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"abstract": "The phase of a single-mode field can be measured in a single-shot measurement\nby interfering the field with an effectively classical local oscillator of\nknown phase. The standard technique is to have the local oscillator detuned\nfrom the system (heterodyne detection) so that it is sometimes in phase and\nsometimes in quadrature with the system over the course of the measurement.\nThis enables both quadratures of the system to be measured, from which the\nphase can be estimated. One of us [H.M. Wiseman, Phys. Rev. Lett. 75, 4587\n(1995)] has shown recently that it is possible to make a much better estimate\nof the phase by using an adaptive technique in which a resonant local\noscillator has its phase adjusted by a feedback loop during the single-shot\nmeasurement. In Ref.~[H.M. Wiseman and R.B. Killip, Phys. Rev. A 56, 944] we\npresented a semiclassical analysis of a particular adaptive scheme, which\nyielded asymptotic results for the phase variance of strong fields. In this\npaper we present an exact quantum mechanical treatment. This is necessary for\ncalculating the phase variance for fields with small photon numbers, and also\nfor considering figures of merit other than the phase variance. Our results\nshow that an adaptive scheme is always superior to heterodyne detection as far\nas the variance is concerned. However the tails of the probability distribution\nare surprisingly high for this adaptive measurement, so that it does not always\nresult in a smaller probability of error in phase-based optical communication.",
"arxiv_id": "quant-ph/9710056",
"authors": [
"H. M. Wiseman"
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"doi": "10.1103/PhysRevA.57.2169",
"title": "Adaptive single-shot phase measurements: The full quantum theory",
"url": "https://arxiv.org/abs/quant-ph/9710056"
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