Quantum uncertainty of optical coherence

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.

💡 Research Summary

The paper introduces and rigorously investigates the notion of quantum uncertainty associated with optical coherence, a property that, unlike amplitude, phase, or polarization, has not previously been examined from a quantum‑mechanical perspective. The authors focus on the first‑order coherence of the simplest possible field—a monochromatic plane wave that is classically perfectly coherent—and treat both scalar (single‑polarization) and vector (two‑polarization) cases.

In the scalar treatment, the first‑order correlation function (G(x_1,x_2)=\mathrm{Tr}