coherences

Coherence is the property of a system in which its components maintain fixed phase relationships, allowing predictable interference effects. In physics, coherence describes the correlation between physical quantities across space or time. Two broad types are temporal coherence, which measures phase stability over time, and spatial coherence, which measures phase correlation across different points in space. Coherence is often discussed in relation to interference: high coherence supports stable, high-contrast fringes, while low coherence leads to washed-out patterns. Related quantities include coherence length, the distance over which the wave maintains a specified degree of coherence, and coherence time, the timescale over which phase information is preserved.

In optics, coherence characterizes light sources. Lasers exhibit high temporal and spatial coherence; thermal or incandescent sources have limited coherence. Spectral width and angular distribution affect coherence. The degree of coherence can be described by correlation functions; first-order coherence g^(1)(tau) measures field amplitude correlations, while second-order coherence g^(2)(tau) relates to intensity correlations and photon statistics.

In quantum mechanics, coherences refer to off-diagonal elements of the density matrix that encode relative phase between quantum states. They enable superposition and interference at the level of populations. Interactions with the environment generally cause decoherence, suppressing off-diagonal terms and driving a system toward classical mixtures. Coherence can be manipulated and consumed as a resource in quantum information tasks, metrology, and spectroscopy, subject to trade-offs with decoherence and noise.