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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Coherence (physics) | 3/4 | https://en.wikipedia.org/wiki/Coherence_(physics) | reference | science, encyclopedia | 2026-05-05T13:41:37.176399+00:00 | kb-cron |
Sometimes people also use "spatial coherence" to refer to the visibility when a wave-like state is combined with a spatially shifted copy of itself.
=== Examples ===
Consider a tungsten light-bulb filament. Different points in the filament emit light independently and have no fixed phase-relationship. In detail, at any point in time the profile of the emitted light is going to be distorted. The profile will change randomly over the coherence time
τ
c
{\displaystyle \tau _{c}}
. Since for a white-light source such as a light-bulb
τ
c
{\displaystyle \tau _{c}}
is small, the filament is considered a spatially incoherent source. In contrast, a radio antenna array, has large spatial coherence because antennas at opposite ends of the array emit with a fixed phase-relationship. Light waves produced by a laser often have high temporal and spatial coherence (though the degree of coherence depends strongly on the exact properties of the laser). Spatial coherence of laser beams also manifests itself as speckle patterns and diffraction fringes seen at the edges of shadow. Holography requires temporally and spatially coherent light. Its inventor, Dennis Gabor, produced successful holograms more than ten years before lasers were invented. To produce coherent light he passed the monochromatic light from an emission line of a mercury-vapor lamp through a pinhole spatial filter. In February 2011 it was reported that helium atoms, cooled to near absolute zero / Bose–Einstein condensate state, can be made to flow and behave as a coherent beam as occurs in a laser.
== Spectral coherence of short pulses ==
Waves of different frequencies (in light these are different colours) can interfere to form a pulse if they have a fixed relative phase-relationship (see Fourier transform). Conversely, if waves of different frequencies are not coherent, then, when combined, they create a wave that is continuous in time (e.g. white light or white noise). The temporal duration of the pulse
Δ
t
{\displaystyle \Delta t}
is limited by the spectral bandwidth of the light
Δ
f
{\displaystyle \Delta f}
according to:
Δ
f
Δ
t
≥
1
{\displaystyle \Delta f\Delta t\geq 1}
, which follows from the properties of the Fourier transform and results in Küpfmüller's uncertainty principle (for quantum particles it also results in the Heisenberg uncertainty principle). If the phase depends linearly on the frequency (i.e.
θ
(
f
)
∝
f
{\displaystyle \theta (f)\propto f}
) then the pulse will have the minimum time duration for its bandwidth (a transform-limited pulse), otherwise it is chirped (see dispersion).
=== Measurement of spectral coherence === Measurement of the spectral coherence of light requires a nonlinear optical interferometer, such as an intensity optical correlator, frequency-resolved optical gating (FROG), or spectral phase interferometry for direct electric-field reconstruction (SPIDER).
== Polarization and coherence ==
Light also has a polarization, which is the direction in which the electric or magnetic field oscillates. Unpolarized light is composed of incoherent light waves with random polarization angles. The electric field of the unpolarized light wanders in every direction and changes in phase over the coherence time of the two light waves. An absorbing polarizer rotated to any angle will always transmit half the incident intensity when averaged over time. If the electric field wanders by a smaller amount the light will be partially polarized so that at some angle, the polarizer will transmit more than half the intensity. If a wave is combined with an orthogonally polarized copy of itself delayed by less than the coherence time, partially polarized light is created. The polarization of a light beam is represented by a vector in the Poincaré sphere. For polarized light the end of the vector lies on the surface of the sphere, whereas the vector has zero length for unpolarized light. The vector for partially polarized light lies within the sphere.
== Quantum coherence ==
The signature property of quantum matter waves, wave interference, relies on coherence. While initially patterned after optical coherence, the theory and experimental understanding of quantum coherence greatly expanded the topic.
=== Matter wave coherence === The simplest extension of optical coherence applies optical concepts to matter waves. For example, when performing the double-slit experiment with atoms instead of light waves, a sufficiently collimated atomic beam creates a coherent atomic wave-function illuminating both slits. Each slit acts as a separate but in-phase beam contributing to the intensity pattern on a screen. These two contributions give rise to an intensity pattern of bright bands due to constructive interference, interlaced with dark bands due to destructive interference, on a downstream screen. Many variations of this experiment have been demonstrated. As with light, transverse coherence (across the direction of propagation) of matter waves is controlled by collimation. Because light, at all frequencies, travels at the same velocity, longitudinal and temporal coherence are linked; in matter waves these are independent. In matter waves, velocity (energy) selection controls longitudinal coherence and pulsing or chopping controls temporal coherence.
=== Quantum optics === The discovery of the Hanbury Brown and Twiss effect – correlation of light upon coincidence – triggered Glauber's creation of uniquely quantum coherence analysis. Classical optical coherence becomes a classical limit for first-order quantum coherence; higher degree of coherence leads to many phenomena in quantum optics.
=== Macroscopic quantum coherence === Macroscopic scale quantum coherence leads to novel phenomena, the so-called macroscopic quantum phenomena. For instance, the laser, superconductivity and superfluidity are examples of highly coherent quantum systems whose effects are evident at the macroscopic scale. The macroscopic quantum coherence, presenting off-diagonal long-range order (ODLRO) for superfluidity, and laser light, is related to first-order (1-body) coherence/ODLRO, while superconductivity is related to second-order coherence/ODLRO. (For fermions, such as electrons, only even orders of coherence/ODLRO are possible.) For bosons, a Bose–Einstein condensate is an example of a system exhibiting macroscopic quantum coherence through a multiple occupied single-particle state. The classical electromagnetic field exhibits macroscopic quantum coherence. The most obvious example is the carrier signal for radio and TV. They satisfy Glauber's quantum description of coherence.