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

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.

5 + 11 pages

References in corpus (4)

• Quantum limits in the measurement of very small displacements in optical images
• Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
• Quantum improvement of time transfer between remote clocks
• Phase space formalism for quantum estimation of Gaussian states

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• Advances in quantum imaging
• Heisenberg-Limited Quantum Lidar for Joint Range and Velocity Estimation
• Approaching maximal precision of Hong-Ou-Mandel interferometry with non-perfect visibility
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• Towards Quantum Limited Spatial Resolution of NV-Diamond Magnetometry