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<title>Spontaneous parametric down-conversion</title>

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Spontaneous parametric down-conversion

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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, signal and idler photons) of lower energy, in accordance with the laws of <a href="Law_of_conservation_of_energy" class="mw-redirect" title="Law of conservation of energy">energy conservation</a> and <a href="Law_of_conservation_of_momentum" class="mw-redirect" title="Law of conservation of momentum">momentum conservation</a>. It is an important process in <a href="Quantum_optics" title="Quantum optics">quantum optics</a>, for the generation of <a href="Photon_entanglement" class="mw-redirect" title="Photon entanglement">entangled photon</a> pairs and of single photons.

<div class="mw-heading mw-heading2"><h2 id="Description">Description</h2></div>

A <a href="Nonlinear_optics" title="Nonlinear optics">nonlinear crystal</a> is used to produce pairs of photons from a <a href="Photon" title="Photon">photon</a> beam. In accordance with conservations of <a href="Energy" title="Energy">energy</a> and <a href="Momentum" title="Momentum">momentum</a>, 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 (<a href="Dispersion_(optics)" title="Dispersion (optics)">dispersion</a>), only certain triplets of frequencies will be <a href="Phase_matching" class="mw-redirect" title="Phase matching">phase-matched</a> so that simultaneous energy and momentum conservation can be achieved. Phase-matching is most commonly achieved using <a href="Birefringence" title="Birefringence">birefringent</a> 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).

<ul><li>If the signal and idler photons share the same polarization with each other and the pump photon, it is deemed Type-0 SPDC.<a href="#cite_note-1">[1]</a></li>

<li>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.</li>

<li>If the signal and idler photons have perpendicular polarizations, it is deemed Type II SPDC.<a href="#cite_note-2">[2]</a></li></ul>

The conversion efficiency of SPDC is typically very low, with the highest efficiency obtained on the order of 4x10−6 incoming photons for <a href="Lithium_niobate#Periodically_poled_lithium_niobate" title="Lithium niobate">periodically poled lithium niobate</a> (PPLN) in waveguides.<a href="#cite_note-3">[3]</a> 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 <a href="Squeezed_coherent_state#Examples" title="Squeezed coherent state">squeezed vacuum</a> that contains only even <a href="Photon" title="Photon">photon</a> number terms. The nondegenerate output of the Type II down converter is a two-mode squeezed vacuum.

<div class="mw-heading mw-heading2"><h2 id="Example">Example</h2></div>

In a commonly used SPDC apparatus design, a strong <a href="Laser_beam" class="mw-redirect" title="Laser beam">laser beam</a>, termed the "pump" beam, is directed at a BBO <a href="Barium_borate" title="Barium borate">(beta-barium borate)</a> or <a href="Lithium_niobate" title="Lithium niobate">lithium niobate</a> 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 <a href="Cone_(geometry)" class="mw-redirect" title="Cone (geometry)">cones</a> 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 xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vert H\rangle \vert V\rangle }">

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<annotation encoding="application/x-tex">{\displaystyle \vert H\rangle \vert V\rangle }</annotation>

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</math><img src="./538988dcf9685630630be307064debee185aa40d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.954ex; height:2.843ex;" alt="{\displaystyle \vert H\rangle \vert V\rangle }" loading="lazy"> and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vert V\rangle \vert H\rangle }">

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<annotation encoding="application/x-tex">{\displaystyle \vert V\rangle \vert H\rangle }</annotation>

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</math><img src="./e80f2ac38645236d68a2178f49662f232e1bdc48.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.954ex; height:2.843ex;" alt="{\displaystyle \vert V\rangle \vert H\rangle }" loading="lazy">, corresponding to polarizations of left-hand side photon, right-hand side photon.<a href="#cite_note-Kwiat1995-4">[4]</a><a href="#cite_note-Zeilinger2010-5">[5]</a>: 205

Another crystal is KDP (<a href="Potassium_dihydrogen_phosphate" class="mw-redirect" title="Potassium dihydrogen phosphate">potassium dihydrogen phosphate</a>) which is mostly used in Type I down conversion, where both photons have the same polarization.<a href="#cite_note-6">[6]</a>

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

<ol><li>Nonlinearity: The <a href="Refractive_index" title="Refractive index">refractive index</a> of the crystal changes with the intensity of the incident light. This is known as the nonlinear optical response.</li>

<li>Periodicity: The crystal has a regular, repeating structure. This is known as the <a href="Crystal_structure" title="Crystal structure">lattice structure</a>, which is responsible for the regular arrangement of the atoms in the crystal.</li>

<li><a href="Optical_anisotropy" class="mw-redirect" title="Optical anisotropy">Optical anisotropy</a> (or birefringence): The crystal has different refractive indices along different crystallographic axes.</li>

<li>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.</li>

<li>High nonlinear coefficient: Large nonlinear coefficient is desirable, this allow to generate a high number of entangled photons.</li>

<li>High <a href="Laser_damage_threshold" title="Laser damage threshold">optical damage threshold</a>: Crystal with high optical damage threshold can endure high intensity of the pumping beam.</li>

<li>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</li>

<li>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.</li></ol>

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

SPDC was demonstrated as early as 1967 by <a href="Stephen_E._Harris" title="Stephen E. Harris">S. E. Harris</a>, M. K. Oshman, and <a href="Robert_L._Byer" title="Robert L. Byer">R. L. Byer</a>,<a href="#cite_note-7">[7]</a> as well as by D. Magde and H. Mahr.<a href="#cite_note-8">[8]</a> It was first applied to experiments related to <a href="Coherence_(physics)" title="Coherence (physics)">coherence</a> by two independent pairs of researchers in the late 1980s: <a href="Carroll_Alley" title="Carroll Alley">Carroll Alley</a> and Yanhua Shih, and <a href="Rupamanjari_Ghosh" title="Rupamanjari Ghosh">Rupamanjari Ghosh</a> and <a href="Leonard_Mandel" title="Leonard Mandel">Leonard Mandel</a>.<a href="#cite_note-9">[9]</a><a href="#cite_note-10">[10]</a> The <a href="Wave%E2%80%93particle_duality" title="Wave–particle duality">duality</a> between incoherent (<a href="Van_Cittert%E2%80%93Zernike_theorem" title="Van Cittert–Zernike theorem">Van Cittert–Zernike theorem</a>) and biphoton emissions was found.<a href="#cite_note-11">[11]</a>

<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

SPDC allows for the creation of <a href="Optical_field" class="mw-redirect" title="Optical field">optical fields</a> 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 <a href="Fock_state" title="Fock state">Fock states</a>).<a href="#cite_note-12">[12]</a> The single photons as well as the photon pairs are often used in <a href="Quantum_information" title="Quantum information">quantum information</a> experiments and applications like <a href="Quantum_cryptography" title="Quantum cryptography">quantum cryptography</a> and <a href="Bell_test_experiments" class="mw-redirect" title="Bell test experiments">Bell test experiments</a>.

SPDC is widely used to create pairs of entangled photons with a high degree of spatial correlation.<a href="#cite_note-WalbornMonken2010-13">[13]</a> Such pairs are used in <a href="Ghost_imaging" title="Ghost imaging">ghost imaging</a>, 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.

<div class="mw-heading mw-heading2"><h2 id="Alternatives">Alternatives</h2></div>

The newly observed effect of <a href="Two-photon_emission" class="mw-redirect" title="Two-photon emission">two-photon emission</a> from electrically driven semiconductors has been proposed as a basis for more efficient sources of entangled photon pairs.<a href="#cite_note-14">[14]</a> Other than SPDC-generated photon pairs, the photons of a semiconductor-emitted pair usually are not identical but have different energies.<a href="#cite_note-15">[15]</a> 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.<a href="#cite_note-16">[16]</a><a href="#cite_note-17">[17]</a>

<ul><li><a href="Photon_upconversion" title="Photon upconversion">Photon upconversion</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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