Journal
PHYSICAL REVIEW A
Volume 79, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.79.053843
Keywords
harmonic oscillators; Heisenberg model; phase locked loops; quantum optics; quantum theory
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Funding
- W. M. Keck Foundation
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We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [M. Tsang , 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 postprocessing 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 counterintuitive, we argue that it does not violate any basic principle of quantum mechanics.
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