Adaptive quantum measurements of a continuously varying phase.

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Author(s)
Berry, DW
Wiseman, HM
Griffith University Author(s)
Year published
2002
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We analyze the problem of quantum-limited estimation of a stochastically varying phase of a continuous beam (rather than a pulse) of the electromagnetic field. We consider both nonadaptive and adaptive measurements, and both dyne detection (using a local oscillator) and interferometric detection. We take the phase variation to be f?=sqrt[?]?(t), where ?(t) is d-correlated Gaussian noise. For a beam of power P, the important dimensionless parameter is N=P/h??, the number of photons per coherence time. For the case of dyne detection, both continuous-wave (cw) coherent beams and cw (broadband) squeezed beams are considered. For ...
View more >We analyze the problem of quantum-limited estimation of a stochastically varying phase of a continuous beam (rather than a pulse) of the electromagnetic field. We consider both nonadaptive and adaptive measurements, and both dyne detection (using a local oscillator) and interferometric detection. We take the phase variation to be f?=sqrt[?]?(t), where ?(t) is d-correlated Gaussian noise. For a beam of power P, the important dimensionless parameter is N=P/h??, the number of photons per coherence time. For the case of dyne detection, both continuous-wave (cw) coherent beams and cw (broadband) squeezed beams are considered. For a coherent beam a simple feedback scheme gives good results, with a phase variance ?N-1/2/2. This is sqrt[2] times smaller than that achievable by nonadaptive (heterodyne) detection. For a squeezed beam a more accurate feedback scheme gives a variance scaling as N-2/3, compared to N-1/2 for heterodyne detection. For the case of interferometry only a coherent input into one port is considered. The locally optimal feedback scheme is identified, and it is shown to give a variance scaling as N-1/2. It offers a significant improvement over nonadaptive interferometry only for N of order unity.
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View more >We analyze the problem of quantum-limited estimation of a stochastically varying phase of a continuous beam (rather than a pulse) of the electromagnetic field. We consider both nonadaptive and adaptive measurements, and both dyne detection (using a local oscillator) and interferometric detection. We take the phase variation to be f?=sqrt[?]?(t), where ?(t) is d-correlated Gaussian noise. For a beam of power P, the important dimensionless parameter is N=P/h??, the number of photons per coherence time. For the case of dyne detection, both continuous-wave (cw) coherent beams and cw (broadband) squeezed beams are considered. For a coherent beam a simple feedback scheme gives good results, with a phase variance ?N-1/2/2. This is sqrt[2] times smaller than that achievable by nonadaptive (heterodyne) detection. For a squeezed beam a more accurate feedback scheme gives a variance scaling as N-2/3, compared to N-1/2 for heterodyne detection. For the case of interferometry only a coherent input into one port is considered. The locally optimal feedback scheme is identified, and it is shown to give a variance scaling as N-1/2. It offers a significant improvement over nonadaptive interferometry only for N of order unity.
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Journal Title
Physical Review A: Atomic, Molecular and Optical Physics
Volume
65
Publisher URI
Copyright Statement
© 2002 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
Subject
Mathematical sciences
Physical sciences
Chemical sciences