# Coherence time

For an electromagnetic wave, the coherence time is the time over which a propagating wave (especially a laser or maser beam) may be considered coherent. In other words, it is the time interval within which its phase is, on average, predictable.

In long-distance transmission systems, the coherence time may be reduced by propagation factors such as dispersion, scattering, and diffraction.

Coherence time, τ, is calculated by dividing the coherence length by the phase velocity of light in a medium; approximately given by

$\tau = \frac{1}{\Delta \nu} \approx \frac{\lambda^2}{c\, \Delta \lambda}$

where λ is the central wavelength of the source, Δν and Δλ is the spectral width of the source in units of frequency and wavelength respectively, and c is the speed of light in vacuum.

A single mode fiber laser has a linewidth of a few kHz. The Schawlow-Townes limit for some cw lasers can be below 1 Hz. Hydrogen masers have linewidth around 1 Hz;[1] their coherence length approximately corresponds to the distance from the Earth to the Moon.

As of 2009, single electron spins show the longest room-temperature spin dephasing times ever observed in solid-state systems (1.8 ms).[2]

## References

1. ^ http://www.physics.harvard.edu/Thesespdfs/humphrey.pdf - Precision measurements with atomic hydrogen masers
2. ^ Balasubramanian et al. (2009). "Direct Ultralong spin coherence time in isotopically engineered diamond". Nature Materials 8: 383. Bibcode:2009NatMa...8..383B. doi:10.1038/nmat2420.