Estimation of a parameter encoded in the modal structure of a light beam: a quantum theory

TL;DR

This paper establishes fundamental quantum limits for estimating mode parameters of light, providing design recipes and practical methods to enhance precision in applications like imaging, spectroscopy, and phase measurement.

Contribution

It derives quantum bounds for mode parameter estimation and offers explicit mode-design strategies for quantum-enhanced measurement precision.

Findings

Quantum limits for mode parameter estimation are established.

Explicit mode-design recipes enable quantum-enhanced precision.

Practical methods applicable to imaging, spectroscopy, and phase estimation.

Abstract

Quantum light is described not only by a quantum state but also by the shape of the electromagnetic modes on which the state is defined. Optical precision measurements often estimate a ``mode parameter'' that determines properties such as frequency, temporal shape and the spatial distribution of the light field. By deriving quantum precision limits, we establish the fundamental bounds for mode parameter estimation. Our results reveal explicit mode-design recipes that enable the estimation of any mode parameter with quantum enhanced precision. Our approach provides practical methods for optimizing mode parameter estimation with relevant applications, including spatial and temporal positioning, spectroscopy, phase estimation, and superresolution imaging.