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arXiv:2212.04547 · Physical Review Research

Bridging coherence optics and classical mechanics: A generic light polarization-entanglement complementary relation

Xiao‐Feng Qian, Misagh Izadi

Published Aug 17, 2023• 11 citations

Abstract

While optics and mechanics are two distinct branches of physics, they are connected. It is well known that the geometrical/ray treatment of light has direct analogies to mechanical descriptions of particle motion. However, connections between coherence wave optics and classical mechanics are rarely reported. Here we report links of the two through a systematic quantitative analysis of polarization and entanglement, two optical coherence properties under the wave description of light pioneered by Huygens and Fresnel. A generic complementary identity relation is obtained for arbitrary light fields. More surprisingly, through the barycentric coordinate system, optical polarization, entanglement, and their identity relation are shown to be quantitatively associated with the mechanical concepts of center of mass and moment of inertia via the Huygens-Steiner theorem for rigid body rotation. The obtained result bridges coherence wave optics and classical mechanics through the two theories of Huygens.

DOI: 10.1103/physrevresearch.5.033110

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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, remains to be considered. 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.