Spontaneous parametric down-conversion
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, a signal photon, and an idler photon) of lower energy, in accordance with the law of conservation of energy and law of conservation of momentum. It is an important process in quantum optics, for the generation of entangled photon pairs, and of single photons. Basic process. A nonlinear crystal is used to split photon beams into pairs of photons that , in accordance with the law of conservation of energy and law of conservation of momentum, have combined energies and momenta equal to the energy and momentum of the original photon and crystal lattice. Because the index of refraction changes with frequency (dispersion), only certain triplets of frequencies will be phase-matched so that simultaneous energy and momentum conservation can be achieved. Phase-matching is most commonly achieved using 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 (the pump) and the  two output photons (signal and idler). If the signal and idler photons share the same polarization with each other and with the destroyed pump photon it is deemed Type-0 SPDC; if the signal and idler photons share the same polarization to 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. The conversion efficiency of SPDC is typically very low, with the highest efficiency obtained on the order of 4 pairs per 10 incoming photons for PPLN in waveguides. However, if  one half of the pair (the "signal") is detected at any time then its partner (the "idler") is known to be present. The degenerate portion of the output of a Type I down converter is a squeezed vacuum that contains only even photon number terms. The degenerate output of the Type II down converter is a two-mode squeezed vacuum. Example. In a commonly used SPDC apparatus design, a strong laser beam, termed the "pump" beam, is directed at a BBO (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 edges of two cones, whose axes are symmetrically arranged relative to the pump beam. Also, due to the conservation of momentum, the two photons are always symmetrically located along the edges of the cones, relative to the pump beam. Importantly, the trajectories of the photon pairs may exist simultaneously in the two lines where the cones intersect. This results in entanglement of the photon pairs whose polarizations are perpendicular. Another crystal is KDP (potassium dihydrogen  phosphate) which is mostly used in Type I down conversion, where both photons have the same polarization. Another way to see the down-conversion through using relatively household items is the following: using a common green laser pointer, and one transparent bottle with olive oil in it, by shining the green laser beam through the olive oil it will scatter red photons showing its path through the olive oil (it does not work with other classic household salad oils). History. SPDC was demonstrated as early as 1967 by S. E. Harris, M. K. Oshman, and R.L. Byer, as well as  by D. Magde and H. Mahr. It was first applied to experiments related to coherence by two independent pairs of researchers in the late 1980s: Carroll Alley and Yanhua Shih, and Rupamanjari Ghosh and Leonard Mandel. The duality between incoherent (Van Cittert–Zernike theorem) and biphoton emissions was found. Applications. SPDC allows for the creation of optical fields 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 states). 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. Such pairs are used in ghost imaging, in which information is combined from two light detectors: a conventional, multi-pixel detector that doesn't 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. Other than SPDC-generated photon pairs, the  photons of a semiconductor-emitted pair usually are not identical but have different energies. 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.