Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous time limit and state-variable approach to phase-locked loop design

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dc.creatorTsang, Mankei
dc.creatorShapiro, Jeffrey H.
dc.creatorLloyd, Seth
dc.date2009-02-18
dc.date2009-05-21
dc.date.accessioned2026-07-07T13:16:40Z
dc.date.available2026-07-07T13:16:40Z
dc.descriptionWe consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [Tsang, Shapiro, and Lloyd, Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design homodyne phase-locked loops that can measure the temporal phase with quantum-limited accuracy. We show that post-processing can further improve the estimation performance, if delay is allowed in the estimation. We also investigate the fundamental uncertainties in the simultaneous estimation of harmonic-oscillator position and momentum via continuous optical phase measurements from the classical estimation theory perspective. In the case of delayed estimation, we find that the inferred uncertainty product can drop below that allowed by the Heisenberg uncertainty relation. Although this result seems counter-intuitive, we argue that it does not violate any basic principle of quantum mechanics.
dc.description11 pages, 6 figures, v2: accepted by PRA
dc.identifierhttps://arxiv.org/abs/0902.3034
dc.identifierhttp://arxiv.org/abs/0902.3034
dc.identifierPhysical Review A 79, 053843 (2009)
dc.identifierdoi:10.1103/PhysRevA.79.053843
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230866
dc.subjectQuantum Physics
dc.titleQuantum theory of optical temporal phase and instantaneous frequency. II. Continuous time limit and state-variable approach to phase-locked loop design
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