dorsal/arxiv
View SchemaAdaptive Quantum Measurements of a Continuously Varying Phase
| Authors | D. W. Berry, H. M. Wiseman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0111013 |
| URL | https://arxiv.org/abs/quant-ph/0111013 |
| DOI | 10.1103/PhysRevA.65.043803 |
| Journal | Phys. Rev. A 65, 043803 (2002) |
Abstract
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 non-adaptive and adaptive measurements, and both dyne detection (using a local oscillator) and interferometric detection. We take the phase variation to be \dot\phi = \sqrt{\kappa}\xi(t), where \xi(t) is \delta-correlated Gaussian noise. For a beam of power P, the important dimensionless parameter is N=P/\hbar\omega\kappa, 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 \simeq 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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"abstract": "We analyze the problem of quantum-limited estimation of a stochastically\nvarying phase of a continuous beam (rather than a pulse) of the electromagnetic\nfield. We consider both non-adaptive and adaptive measurements, and both dyne\ndetection (using a local oscillator) and interferometric detection. We take the\nphase variation to be \\dot\\phi = \\sqrt{\\kappa}\\xi(t), where \\xi(t) is\n\\delta-correlated Gaussian noise. For a beam of power P, the important\ndimensionless parameter is N=P/\\hbar\\omega\\kappa, the number of photons per\ncoherence time. For the case of dyne detection, both continuous-wave (cw)\ncoherent beams and cw (broadband) squeezed beams are considered. For a coherent\nbeam a simple feedback scheme gives good results, with a phase variance \\simeq\nN^{-1/2}/2. This is \\sqrt{2} times smaller than that achievable by nonadaptive\n(heterodyne) detection. For a squeezed beam a more accurate feedback scheme\ngives a variance scaling as N^{-2/3}, compared to N^{-1/2} for heterodyne\ndetection. For the case of interferometry only a coherent input into one port\nis considered. The locally optimal feedback scheme is identified, and it is\nshown to give a variance scaling as N^{-1/2}. It offers a significant\nimprovement over nonadaptive interferometry only for N of order unity.",
"arxiv_id": "quant-ph/0111013",
"authors": [
"D. W. Berry",
"H. M. Wiseman"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.043803",
"journal_ref": "Phys. Rev. A 65, 043803 (2002)",
"title": "Adaptive Quantum Measurements of a Continuously Varying Phase",
"url": "https://arxiv.org/abs/quant-ph/0111013"
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