Quantum uncertainty of optical coherence

TL;DR

This paper introduces the concept of quantum optical coherence uncertainty, revealing that all states except number states exhibit coherence fluctuations, which has implications for high-precision optical measurements.

Contribution

It formulates the quantum uncertainty of optical coherence and establishes uncertainty relations depending on polarization and space-time, advancing fundamental understanding of light's quantum properties.

Findings

Number states have zero coherence uncertainty.

All other states exhibit coherence fluctuations.

Uncertainty relations depend on polarization and space-time.

Abstract

Light is known to exhibit quantum uncertainty in terms of its amplitude, phase, and polarization. However, quantum uncertainty related to coherence, which is also a fundamental physical property of light, has not been considered to date. Here, we formulate and explore the concept of quantum optical coherence uncertainty. We focus on the first-order coherence of the simplest possible light field, a purely monochromatic plane wave, which is classically completely stable. Starting from a scalar treatment, we show that the field displays zero coherence uncertainty only for a number state. We then proceed to the vectorial regime and establish that any state leads to coherence fluctuations, governed by a set of uncertainty relations depending on the polarization state and space-time points. Our work thus provides fundamental insights into the quantum character of optical coherence, with potential benefits in applications using highly sensitive interferometric and polarimetric techniques.