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Conference on Lasers and Electro-Optics

Quantum Optical Temporal Phase Estimation by Homodyne Phase-Locked Loops

Mankei Tsang, Jeffrey H. Shapiro, Seth Lloyd

Published Jan 1, 2009• 4 citations
Publisher

Abstract

Using classical estimation techniques, we design homodyne phase-locked loops for optical temporal phase and instantaneous frequency measurements at the quantum limit.
DOI
10.1364/iqec.2009.itui6

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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 et al., 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.
We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited measurements of temporal phase and instantaneous frequency. Standard and Heisenberg quantum limits to such measurements are then derived. For optical sensing applications, we propose multipass and Fabry-P\'erot position and velocity sensors that take advantage of the signal-to-noise-ratio enhancement effect of wide-band angle modulation without requiring nonclassical light. We also generalize our theory to three spatial dimensions for nonrelativistic bosons and define a Hermitian fluid velocity operator, which provides a theoretical underpinning to the current-algebra approach of quantum hydrodynamics.