Editing Spontaneous parametric down-conversion (section)

== 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.