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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 In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means that ...
and law of conservation of momentum. It is an important process in
quantum optics Quantum optics is a branch of atomic, molecular, and optical physics dealing with how individual quanta of light, known as photons, interact with atoms and molecules. It includes the study of the particle-like properties of photons. Photons have b ...
, for the generation of entangled photon pairs, and of single photons.


Basic process

A nonlinear crystal is used to produce pairs of photons from a
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...
beam. In accordance with the
law of conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means that ...
and law of conservation of momentum, the pairs have combined energies and momenta equal to the energy and momentum of the original photon. 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 106 incoming photons for PPLN in waveguides. 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 vacuum In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues. Examples are position x and momentum p of a particle, and the (dimension-less) electr ...
that contains only even
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...
number terms. The nondegenerate 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 A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The firs ...
, termed the "pump" beam, is directed at a BBO (beta-barium borate) or
lithium niobate Lithium niobate () is a non-naturally-occurring salt consisting of niobium, lithium, and oxygen. Its single crystals are an important material for optical waveguides, mobile phones, piezoelectric sensors, optical modulators and various other linea ...
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 A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines ...
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 , H>, V> and , V>, H>, corresponding to polarizations of left-hand side photon, right-hand side photon. 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 Stephen Ernest Harris (born November 29, 1936) is an American physicist known for his contributions to electromagnetically induced transparency (EIT), modulation of single photons, and x-ray emission. In a diverse career, he has collaborated w ...
, 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 Rupamanjari Ghosh was the second Vice-Chancellor (1 February 2016 - 31 January 2022) of Shiv Nadar University, Uttar Pradesh, India. She is also the former founding Director of School of Natural Sciences and founding Dean of Research & Graduate S ...
and Leonard Mandel. The duality between incoherent ( Van Cittert–Zernike theorem) and biphoton emissions was found.


Applications

SPDC allows for the creation of
optical field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
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 In quantum mechanics, a Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta). These states are named after the Soviet physicist Vladimir Fock. Fock states play an imp ...
s). The single photons as well as the photon pairs are often used in
quantum information Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...
experiments and applications like
quantum cryptography Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution ...
and
Bell test experiments A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism. Named for John Stewart Bell, the e ...
. 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.


See also

*
Photon upconversion A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...


References

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