Editing Shot noise (section)

===Optics ===
In [[optics]], shot noise describes the fluctuations of the number of photons detected (or simply counted in the abstract) because they occur independently of each other. This is therefore another consequence of discretization, in this case of the energy in the electromagnetic field in terms of photons. In the case of photon ''detection'', the relevant process is the random conversion of photons into photo-electrons for instance, thus leading to a larger effective shot noise level when using a detector with a [[quantum efficiency]] below unity. Only in an exotic [[squeezed coherent state]] can the number of photons measured per unit time have fluctuations smaller than the square root of the expected number of photons counted in that period of time. Of course there are other mechanisms of noise in optical signals which often dwarf the contribution of shot noise. When these are absent, however, optical detection is said to be "photon noise limited" as only the shot noise (also known as "[[quantum noise]]" or "photon noise" in this context) remains.

Shot noise is easily observable in the case of  [[photomultiplier]]s and [[avalanche photodiodes]] used in the Geiger mode, where individual photon detections are observed. However the same noise source is present with higher light intensities measured by any [[photo detector]], and is directly measurable when it dominates the noise of the subsequent electronic amplifier. Just as with other forms of shot noise, the fluctuations in a photo-current due to shot noise scale as the square-root of the average intensity:

:<math>(\Delta I)^2 \ \stackrel{\mathrm{def}}{=}\   \langle\left(I-\langle I\rangle
\right)^2\rangle \propto I. </math>

The shot noise of a coherent optical beam (having no other noise sources) is a fundamental physical phenomenon, reflecting [[quantum fluctuation]]s in the electromagnetic field. In [[Homodyne detection|optical homodyne detection]], the shot noise in the photodetector can be attributed to either the [[Vacuum fluctuation|zero point fluctuations]] of the quantised electromagnetic field, or to the discrete nature of the photon absorption process.<ref>{{Cite journal|last=Carmichael|first=H. J.|date=1987-10-01|title=Spectrum of squeezing and photocurrent shot noise: a normally ordered treatment|journal=JOSA B|language=EN|volume=4|issue=10|pages=1588–1603|doi=10.1364/JOSAB.4.001588|issn=1520-8540|bibcode=1987JOSAB...4.1588C}}</ref> However, shot noise itself is not a distinctive feature of quantised field and can also be explained through [[Semiclassical physics|semiclassical theory]]. What the semiclassical theory does not predict, however, is the [[Squeezed coherent state|squeezing]] of shot noise.<ref>{{Cite book|title=Optical coherence and quantum optics|last=Leonard.|first=Mandel|date=1995|publisher=Cambridge University Press|others=Wolf, Emil.|isbn=9780521417112|location=Cambridge|oclc=855969014}}</ref> Shot noise also sets a lower bound on the noise introduced by [[quantum amplifier]]s which preserve the phase of an optical signal.