langdistancekohærens

Langdistancekohærens, or long-distance coherence, describes the persistence of a well-defined phase relation in a wave or quantum state across substantial spatial separations. It enables observable interference between distant parts of a system and is commonly quantified by coherence functions such as the first-order coherence g^(1)(r1, r2) or by a corresponding coherence time and length. The coherence length Lc and coherence time τc indicate over what distance and time the phase relation remains correlated.

In optics, sources with long-range spatial coherence, like lasers, produce well-defined interference patterns over large apertures, while incoherent sources yield short coherence lengths. In condensed matter and quantum systems, long-range phase coherence is associated with macroscopic quantum order, as in superconductors and superfluids, where a single phase governs the system across macroscopic distances. In astronomy, long-distance coherence enables interferometric techniques that combine light from separate telescopes to achieve higher angular resolution.

Measurement and interpretation rely on interferometry and spectral analysis. Interferometers probe g^(1)(r1, r2) by comparing signals from two paths; spectral bandwidth Δν relates to coherence time via τc ≈ 1/Δν. The van Cittert–Zernike theorem links source size to spatial coherence, informing imaging and metrology.

Applications span high-precision metrology, optical imaging, and quantum information, where preserving coherence over distance improves performance. Challenges include environmental noise, temperature, interactions, and disorder that cause dephasing. Techniques to mitigate decoherence encompass isolation, cooling, and dynamical decoupling.