Editing Spontaneous parametric down-conversion

{{Short description|Optical process}}
[[Image:Spontaneous Parametric Downconversion.png|thumb|350px|Schematic of SPDC process. Note that conservation laws are with respect to energy and momentum ''inside'' the crystal.]]
'''Spontaneous parametric down-conversion''' (also known as '''SPDC''', '''parametric fluorescence''' or '''parametric scattering''') is a nonlinear instant optical process that converts one photon of higher energy (namely, a ''pump'' photon) into a pair of photons (namely, ''signal'' and ''idler'' photons) of lower energy, in accordance with the laws of [[law of conservation of energy|energy conservation]] and [[law of conservation of momentum|momentum conservation]]. It is an important process in [[quantum optics]], for the generation of [[photon entanglement|entangled photon]] pairs and of single photons.

==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.

== Example ==
[[File:SPDC figure.png|thumb|right|350px|An SPDC scheme with the Type II output]]

In a commonly used SPDC apparatus design, a strong [[laser beam]], termed the "pump" beam, is directed at a BBO [[Barium borate|(beta-barium borate)]] or [[lithium niobate]] crystal. Most of the photons continue straight through the crystal. However, occasionally, some of the photons undergo spontaneous down-conversion with Type II polarization correlation, and the resultant correlated photon pairs have trajectories that are constrained along the sides of two [[cone (geometry)|cone]]s whose axes are symmetrically arranged relative to the pump beam. Due to the conservation of momentum, the two photons are always symmetrically located on the sides of the cones, relative to the pump beam. In particular, the trajectories of a small proportion of photon pairs will lie simultaneously on the two lines where the surfaces of the two cones intersect. This results in entanglement of the polarizations of the pairs of photons emerging on those two lines. The photon pairs are in an equal weight quantum superposition of the unentangled states <math> \vert H \rangle\vert V \rangle </math> and <math> \vert V \rangle \vert H\rangle </math>, corresponding to polarizations of left-hand side photon, right-hand side photon.<ref name="Kwiat1995">{{cite journal|author1-link=Paul Kwiat |author=P. Kwiat|title=New High-Intensity Source of Polarization-Entangled Photon Pairs |journal=Phys. Rev. Lett. |volume=75 |issue=24 |pages=4337–4341 |year=1995 |bibcode = 1995PhRvL..75.4337K |doi = 10.1103/PhysRevLett.75.4337 |display-authors=etal |pmid=10059884|doi-access=free }}</ref><ref name="Zeilinger2010">{{cite book|author=Anton Zeilinger|title=Dance of the Photons: From Einstein to Quantum Teleportation|date=12 October 2010|publisher=Farrar, Straus and Giroux|isbn=978-1-4299-6379-4 | chapter =The super-source and closing the communication loophole}}</ref>{{rp|205}}

Another crystal is KDP ([[potassium dihydrogen phosphate]]) which is mostly used in Type I down conversion, where both photons have the same polarization.<ref>{{citation | author = Reck, M H A | title = Quantum Interferometry with Multiports: Entangled Photons in Optical Fibers (page 115) | url=http://www.univie.ac.at/qfp/publications/thesis/mrdiss.pdf |access-date=16 February 2014}}</ref>

Some of the characteristics of effective parametric down-converting nonlinear crystals include:

# Nonlinearity: The [[refractive index]] of the crystal changes with the intensity of the incident light. This is known as the nonlinear optical response.
# Periodicity: The crystal has a regular, repeating structure. This is known as the [[Crystal structure|lattice structure]], which is responsible for the regular arrangement of the atoms in the crystal.
# [[Optical anisotropy]] (or birefringence): The crystal has different refractive indices along different crystallographic axes.
# Temperature and pressure sensitivity: The nonlinearity of the crystal can change with temperature and pressure, and thus the crystal should be kept in a stable temperature and pressure environment.
# High nonlinear coefficient: Large nonlinear coefficient is desirable, this allow to generate a high number of entangled photons.
# High [[Laser damage threshold|optical damage threshold]]: Crystal with high optical damage threshold can endure high intensity of the pumping beam.
# Transparency in the desired wavelength range: It is important for the crystal to be transparent in the wavelength range of the pump beam for efficient nonlinear interactions
# High optical quality and low absorption: The crystal should be high optical quality and low absorption to minimize loss of the pump beam and the generated entangled photons.

== History ==
SPDC was demonstrated as early as 1967 by [[Stephen E. Harris|S. E. Harris]], M. K. Oshman, and [[Robert L. Byer|R. L. Byer]],<ref>{{Cite journal|last1=Harris|first1=S. E.|last2=Oshman|first2=M. K.|last3=Byer|first3=R. L.|date=1967-05-01|title=Observation of Tunable Optical Parametric Fluorescence|url=https://link.aps.org/doi/10.1103/PhysRevLett.18.732|journal=Physical Review Letters|volume=18|issue=18|pages=732–734|doi=10.1103/PhysRevLett.18.732|url-access=subscription}}</ref> as well as by D. Magde and H. Mahr.<ref>{{Cite journal|last1=Magde|first1=Douglas|last2=Mahr|first2=Herbert|date=1967-05-22|title=Study in Ammonium Dihydrogen Phosphate of Spontaneous Parametric Interaction Tunable from 4400 to 16 000 \AA{}|url=https://link.aps.org/doi/10.1103/PhysRevLett.18.905|journal=Physical Review Letters|volume=18|issue=21|pages=905–907|doi=10.1103/PhysRevLett.18.905|url-access=subscription}}</ref> It was first applied to experiments related to [[Coherence (physics)|coherence]] by two independent pairs of researchers in the late 1980s: [[Carroll Alley]] and Yanhua Shih, and [[Rupamanjari Ghosh]] and [[Leonard Mandel]].<ref>Y. Shih and C. Alley, in ''Proceedings of the 2nd Int'l Symposium on Foundations of QM in Light of New Technology'', Namiki et al., eds., Physical Society of Japan, Tokyo, 1986.</ref><ref>{{cite journal | last1 = Ghosh | first1 = R. | last2 = Mandel | first2 = L. | year = 1987 | title = Observation of Nonclassical Effects in the Interference of Two Photons | journal = Phys. Rev. Lett. | volume = 59 | issue = 17| pages = 1903–1905 | doi=10.1103/physrevlett.59.1903| pmid = 10035364 | bibcode = 1987PhRvL..59.1903G }}</ref> The [[Wave–particle duality|duality]] between incoherent ([[Van Cittert–Zernike theorem]]) and biphoton emissions was found.<ref>http://pra.aps.org/abstract/PRA/v62/i4/e043816 - Duality between partial coherence and partial entanglement</ref>

== Applications ==

SPDC allows for the creation of [[optical field]]s containing (to a good approximation) a single photon.  As of 2005, this is the predominant mechanism for an experimenter to create single photons (also known as [[Fock state]]s).<ref>{{cite journal
 | last1 =Zavatta
 | first1 =Alessandro
 | last2 =Viciani
 | first2 =Silvia
 | last3 =Bellini
 | first3 =Marco
 | title =Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection
 | journal =Physical Review A
 | volume =70
 | issue =5
 | pages =053821
 | year =2004
 | doi =10.1103/PhysRevA.70.053821
|arxiv = quant-ph/0406090 |bibcode = 2004PhRvA..70e3821Z | s2cid =119387795
 }}</ref> The single photons as well as the photon pairs are often used in [[quantum information]] experiments and applications like [[quantum cryptography]] and [[Bell test experiments]].

SPDC is widely used to create pairs of entangled photons with a high degree of spatial correlation.<ref name="WalbornMonken2010">{{cite journal |last1=Walborn |first1=S.P. |last2=Monken |first2=C.H. |last3=Pádua|first3=S. |last4=Souto Ribeiro|first4=P.H. |title=Spatial correlations in parametric down-conversion |journal=Physics Reports |volume=495 |issue=4–5 |year=2010 |pages=87–139 |issn=0370-1573 |doi=10.1016/j.physrep.2010.06.003 |arxiv=1010.1236 |bibcode=2010PhR...495...87W |s2cid=119221135 }}</ref> Such pairs are used in [[ghost imaging]], in which information is combined from two light detectors: a conventional, multi-pixel detector that does not view the object, and a single-pixel (bucket) detector that does view the object.

== Alternatives ==
The newly observed effect of [[two-photon emission]] from electrically driven semiconductors has been proposed as a basis for more efficient sources of entangled photon pairs.<ref>{{cite journal | last1=Hayat | first1=Alex | last2=Ginzburg | first2=Pavel | last3=Orenstein | first3=Meir | title=Observation of two-photon emission from semiconductors | journal=Nature Photonics | publisher=Springer Science and Business Media LLC | volume=2 | issue=4 | date=2008-03-02 | issn=1749-4885 | doi=10.1038/nphoton.2008.28 | pages=238–241}}</ref> Other than SPDC-generated photon pairs, the photons of a semiconductor-emitted pair usually are not identical but have different energies.<ref>{{Cite journal|doi=10.1051/0004-6361:20053988|arxiv=astro-ph/0508144|title=Induced two-photon decay of the 2s level and the rate of cosmological hydrogen recombination|journal=Astronomy and Astrophysics|volume=446|issue=1|pages=39–42|year=2006|last1=Chluba|first1=J.|last2=Sunyaev|first2=R. A.|bibcode=2006A&A...446...39C|s2cid=119526307 }}</ref> Until recently, within the constraints of quantum uncertainty, the pair of emitted photons were assumed to be co-located: they are born from the same location. However, a new nonlocalized mechanism for the production of correlated photon pairs in SPDC has highlighted that occasionally the individual photons that constitute the pair can be emitted from spatially separated points.<ref>{{Cite journal|last1=Forbes|first1=Kayn A.|last2=Ford|first2=Jack S.|last3=Andrews|first3=David L.|date=2017-03-30|title=Nonlocalized Generation of Correlated Photon Pairs in Degenerate Down-Conversion|journal=Physical Review Letters|volume=118|issue=13|pages=133602|doi=10.1103/PhysRevLett.118.133602|pmid=28409956|bibcode=2017PhRvL.118m3602F|url=https://ueaeprints.uea.ac.uk/63173/1/PhysRevLett.118.133602.pdf}}</ref><ref>{{Cite journal|last1=Forbes|first1=Kayn A.|last2=Ford|first2=Jack S.|last3=Jones|first3=Garth A.|last4=Andrews|first4=David L.|date=2017-08-23|title=Quantum delocalization in photon-pair generation|journal=Physical Review A|volume=96|issue=2|pages=023850|doi=10.1103/PhysRevA.96.023850|bibcode=2017PhRvA..96b3850F|url=https://ueaeprints.uea.ac.uk/64664/1/Quantum_delocalization_in_photon_pair_generation.pdf}}</ref>

== See also ==

* [[Photon upconversion]]

==References==
{{reflist|30em}}

{{DEFAULTSORT:Spontaneous Parametric Down-Conversion}}
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