Coherence (physics)

In physics, coherence describes the properties of waves that allow for them to exhibit interference. More specifically, it quantifies the degree to which a wave is able to maintain a definite phase relationship. High coherence implies that the wave's phase is highly correlated at different points in space and/or time, enabling clear and strong interference effects. Conversely, low coherence implies weak or absent interference.

Coherence is generally divided into two primary types: temporal coherence and spatial coherence.

• Temporal Coherence: Also known as longitudinal coherence, temporal coherence describes the correlation between the phase of a wave at different points in time. A wave with high temporal coherence maintains a stable phase over a relatively long duration. The coherence time (and its related coherence length) quantify the duration (or distance) over which the wave maintains a predictable phase. Monochromatic light sources tend to exhibit high temporal coherence. The coherence time is inversely proportional to the bandwidth of the source. A perfectly monochromatic source would have infinite temporal coherence.

• Spatial Coherence: Also known as transverse coherence, spatial coherence describes the correlation between the phase of a wave at different points in space at a given time. A wave with high spatial coherence maintains a stable phase across a relatively large area. This is particularly relevant for beams of light, where spatial coherence describes the uniformity of the phase across the beam's cross-section. A perfectly coherent beam would have a uniform phase front. Point sources, or sources that appear as point sources from a distance, tend to exhibit high spatial coherence.

The concept of coherence is fundamental to many areas of physics, including optics, acoustics, and quantum mechanics. It plays a critical role in applications such as holography, interferometry, laser technology, and medical imaging. The degree of coherence is often quantified by a coherence function, which mathematically describes the correlation between the wave's phase at different points. The normalized coherence function ranges from 0 (completely incoherent) to 1 (perfectly coherent).

In quantum mechanics, the concept of coherence extends to the superposition of quantum states. A coherent superposition refers to a superposition where the relative phases between the different states are well-defined and stable, leading to observable interference effects. Decoherence, the loss of coherence, is a key process that explains the emergence of classical behavior from quantum systems.