Quantum theory of optical temporal phase and instantaneous frequency

TL;DR

This paper develops a quantum theory for optical phase and frequency measurement in the time domain, introducing homodyne phase-locked loops and applying the theory to optical sensing and quantum hydrodynamics.

Contribution

It presents a comprehensive quantum framework for optical phase and frequency, including measurement limits, sensor designs, and a three-dimensional generalization for bosonic fluids.

Findings

Derived quantum limits for phase and frequency measurements.

Proposed multipass and Fabry-Pérot sensors enhancing SNR without nonclassical light.

Extended theory to three spatial dimensions with a fluid velocity operator.

Abstract

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 wideband angle modulation without requiring nonclassical light. We also generalize our theory to three spatial dimensions for nonrelativistic bosons and define an Hermitian fluid velocity operator, which provides a theoretical underpinning to the current-algebra approach of quantum hydrodynamics.