Editing Spontaneous parametric down-conversion (section)

==Description==
[[File:Scheme of spontaneous parametric down-conversion.pdf|thumb|right|350px|An SPDC scheme with the Type I output]]
[[File:Vacuum fluctuations revealed through spontaneous parametric down-conversion.ogv|thumb|right|350px|The video of an experiment showing [[vacuum fluctuations]] (in the red ring) amplified by SPDC (corresponding to the image above)]]

A [[Nonlinear optics|nonlinear crystal]] is used to produce pairs of photons from a [[photon]] beam. In accordance with conservations of [[energy]] and [[momentum]], the pairs need to have combined energies and momenta equal to the energy and momentum of the original photon. Because the index of refraction changes with frequency ([[Dispersion (optics)|dispersion]]), only certain triplets of frequencies will be [[phase matching|phase-matched]] so that simultaneous energy and momentum conservation can be achieved. Phase-matching is most commonly achieved using [[Birefringence|birefringent]] nonlinear materials, whose index of refraction changes with polarization. As a result of this, different types of SPDC are categorized by the polarizations of the input photon (''pump'') and the two output photons (''signal'' and ''idler'').

* If the signal and idler photons share the same polarization with each other and the pump photon is destroyed, it is deemed Type-0 SPDC.<ref>{{Cite journal|last1=Lerch|first1=Stefan|last2=Bessire|first2=Bänz|last3=Bernhard|first3=Christof|last4=Feurer|first4=Thomas|last5=Stefanov|first5=André|date=2013-04-01|title=Tuning curve of type-0 spontaneous parametric down-conversion|journal=Journal of the Optical Society of America B|volume=30|issue=4|pages=953–958|doi=10.1364/JOSAB.30.000953|issn=0740-3224|arxiv=1404.1192|bibcode=2013JOSAB..30..953L|s2cid=149192 }}</ref>
* If the signal and idler photons share the same polarization with each other, but are orthogonal to the pump polarization, it is Type-I SPDC.
* If the signal and idler photons have perpendicular polarizations, it is deemed Type II SPDC.<ref>{{Cite book|title=Nonlinear Optics, Third Edition|url=https://archive.org/details/nonlinearopticst00boyd|url-access=limited|last=Boyd|first=Robert|publisher=Academic Press|year=2008|isbn=978-0-12-369470-6|location=New York|pages=[https://archive.org/details/nonlinearopticst00boyd/page/n90 79]–88}}</ref>

The conversion efficiency of SPDC is typically very low, with the highest efficiency obtained on the order of 4x10<sup>−6</sup> incoming photons for [[PPLN]] in waveguides.<ref>{{cite journal|first1=Matthias|last1=Bock|first2=Andreas|last2=Lenhard|first3=Christopher|last3=Chunnilall|first4=Christoph|last4=Becher|title=Highly efficient heralded single-photon source for telecom wavelengths based on a PPLN waveguide|journal=Optics Express|date=17 October 2016|issn=1094-4087|pages=23992–24001|volume=24|issue=21|doi=10.1364/OE.24.023992|pmid=27828232|bibcode=2016OExpr..2423992B|doi-access=free}}</ref> However, if one half of the pair is detected at any time then its partner is known to be present. The degenerate portion of the output of a Type I down converter is a [[Squeezed coherent state#Examples|squeezed vacuum]] that contains only even [[photon]] number terms. The nondegenerate output of the Type II down converter is a two-mode squeezed vacuum.