Spontaneous parametric down-conversion

Last updated
Schematic of SPDC process. Note that conservation laws are with respect to energy and momentum inside the crystal. Spontaneous Parametric Downconversion.png
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, 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.

Contents

Basic process

An SPDC scheme with the Type I output Scheme of spontaneous parametric down-conversion.pdf
An SPDC scheme with the Type I output
The video of an experiment showing vacuum fluctuations (in the red ring) amplified by SPDC (corresponding to the image above)

A nonlinear crystal is used to produce pairs of photons from a photon beam. In accordance with the law of conservation of energy 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; [1] 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; and if the signal and idler photons have perpendicular polarizations, it is deemed Type II SPDC. [2]

The conversion efficiency of SPDC is typically very low, with the highest efficiency obtained on the order of 4x10-6 incoming photons for PPLN in waveguides. [3] 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 that contains only even photon number terms. The nondegenerate output of the Type II down converter is a two-mode squeezed vacuum.

Example

An SPDC scheme with the Type II output SPDC figure.png
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 (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 cones 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 and , corresponding to polarizations of left-hand side photon, right-hand side photon. [4] [5] : 205 

Another crystal is KDP (potassium dihydrogen phosphate) which is mostly used in Type I down conversion, where both photons have the same polarization. [6]

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

  1. Nonlinearity: The refractive index of the crystal changes with the intensity of the incident light. This is known as the nonlinear optical response.
  2. Periodicity: The crystal has a regular, repeating structure. This is known as the lattice structure, which is responsible for the regular arrangement of the atoms in the crystal.
  3. Optical anisotropy: The crystal has different refractive indices along different crystallographic axes.
  4. 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.
  5. High nonlinear coefficient: Large nonlinear coefficient is desirable, this allow to generate a high number of entangled photons.
  6. High optical damage threshold: Crystal with high optical damage threshold can endure high intensity of the pumping beam.
  7. 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
  8. 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 S. E. Harris, M. K. Oshman, and R. L. Byer, [7] as well as by D. Magde and H. Mahr. [8] 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. [9] [10] The duality between incoherent (Van Cittert–Zernike theorem) and biphoton emissions was found. [11]

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). [12] 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. [13] 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. [14] Other than SPDC-generated photon pairs, the photons of a semiconductor-emitted pair usually are not identical but have different energies. [15] 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. [16] [17]

See also

Related Research Articles

<span class="mw-page-title-main">Nonlinear optics</span> Branch of physics

Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (when the electric field of the light is >108 V/m and thus comparable to the atomic electric field of ~1011 V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear. In nonlinear optics, the superposition principle no longer holds.

<span class="mw-page-title-main">Quantum entanglement</span> Correlation between quantum systems

Quantum entanglement is the phenomenon of a group of particles being generated, interacting, or sharing spatial proximity in such a way that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.

<span class="mw-page-title-main">Squeezed coherent state</span> Type of quantum state

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 and momentum of a particle, and the (dimension-less) electric field in the amplitude and in the mode of a light wave. The product of the standard deviations of two such operators obeys the uncertainty principle:

Four-wave mixing (FWM) is an intermodulation phenomenon in nonlinear optics, whereby interactions between two or three wavelengths produce two or one new wavelengths. It is similar to the third-order intercept point in electrical systems. Four-wave mixing can be compared to the intermodulation distortion in standard electrical systems. It is a parametric nonlinear process, in that the energy of the incoming photons is conserved. FWM is a phase-sensitive process, in that the efficiency of the process is strongly affected by phase matching conditions.

<span class="mw-page-title-main">Optical parametric oscillator</span>

An optical parametric oscillator (OPO) is a parametric oscillator that oscillates at optical frequencies. It converts an input laser wave with frequency into two output waves of lower frequency by means of second-order nonlinear optical interaction. The sum of the output waves' frequencies is equal to the input wave frequency: . For historical reasons, the two output waves are called "signal" and "idler", where the output wave with higher frequency is the "signal". A special case is the degenerate OPO, when the output frequency is one-half the pump frequency, , which can result in half-harmonic generation when signal and idler have the same polarization.

In quantum mechanics, a quantum eraser experiment is an interferometer experiment that demonstrates several fundamental aspects of quantum mechanics, including quantum entanglement and complementarity. The quantum eraser experiment is a variation of Thomas Young's classic double-slit experiment. It establishes that when action is taken to determine which of 2 slits a photon has passed through, the photon cannot interfere with itself. When a stream of photons is marked in this way, then the interference fringes characteristic of the Young experiment will not be seen. The experiment also creates situations in which a photon that has been "marked" to reveal through which slit it has passed can later be "unmarked." A photon that has been "unmarked" will interfere with itself once again, restoring the fringes characteristic of Young's experiment.

A delayed-choice quantum eraser experiment, first performed by Yoon-Ho Kim, R. Yu, S. P. Kulik, Y. H. Shih and Marlan O. Scully, and reported in early 1998, is an elaboration on the quantum eraser experiment that incorporates concepts considered in John Archibald Wheeler's delayed-choice experiment. The experiment was designed to investigate peculiar consequences of the well-known double-slit experiment in quantum mechanics, as well as the consequences of quantum entanglement.

<span class="mw-page-title-main">Optical lattice</span> Atomic-scale structure formed through the Stark shift by opposing beams of light

An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate at the potential extrema. The resulting arrangement of trapped atoms resembles a crystal lattice and can be used for quantum simulation.

In quantum optics, a NOON state or N00N state is a quantum-mechanical many-body entangled state:

In physics, a quantum amplifier is an amplifier that uses quantum mechanical methods to amplify a signal; examples include the active elements of lasers and optical amplifiers.

In quantum information and quantum computing, a cluster state is a type of highly entangled state of multiple qubits. Cluster states are generated in lattices of qubits with Ising type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. They are different from other types of entangled states such as GHZ states or W states in that it is more difficult to eliminate quantum entanglement in the case of cluster states. Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice. Cluster states are especially useful in the context of the one-way quantum computer. For a comprehensible introduction to the topic see.

Quantum imaging is a new sub-field of quantum optics that exploits quantum correlations such as quantum entanglement of the electromagnetic field in order to image objects with a resolution or other imaging criteria that is beyond what is possible in classical optics. Examples of quantum imaging are quantum ghost imaging, quantum lithography, imaging with undetected photons, sub-shot-noise imaging, and quantum sensing. Quantum imaging may someday be useful for storing patterns of data in quantum computers and transmitting large amounts of highly secure encrypted information. Quantum mechanics has shown that light has inherent “uncertainties” in its features, manifested as moment-to-moment fluctuations in its properties. Controlling these fluctuations—which represent a sort of “noise”—can improve detection of faint objects, produce better amplified images, and allow workers to more accurately position laser beams.

Ghost imaging is a technique that produces an image of an object by combining information 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. Two techniques have been demonstrated. A quantum method uses a source of pairs of entangled photons, each pair shared between the two detectors, while a classical method uses a pair of correlated coherent beams without exploiting entanglement. Both approaches may be understood within the framework of a single theory.

Hardy's paradox is a thought experiment in quantum mechanics devised by Lucien Hardy in 1992–1993 in which a particle and its antiparticle may interact without annihilating each other.

Nonlinear photonic crystals are usually used as quasi-phase-matching materials. They can be one-dimensional, two-dimensional or three-dimensional.

<span class="mw-page-title-main">Orbital angular momentum of light</span> Type of angular momentum in light

The orbital angular momentum of light (OAM) is the component of angular momentum of a light beam that is dependent on the field spatial distribution, and not on the polarization. It can be further split into an internal and an external OAM. The internal OAM is an origin-independent angular momentum of a light beam that can be associated with a helical or twisted wavefront. The external OAM is the origin-dependent angular momentum that can be obtained as cross product of the light beam position and its total linear momentum.

Linear optical quantum computing or linear optics quantum computation (LOQC), also photonic quantum computing (PQC), is a paradigm of quantum computation, allowing (under certain conditions, described below) universal quantum computation. LOQC uses photons as information carriers, mainly uses linear optical elements, or optical instruments (including reciprocal mirrors and waveplates) to process quantum information, and uses photon detectors and quantum memories to detect and store quantum information.

Gray molasses is a method of sub-Doppler laser cooling of atoms. It employs principles from Sisyphus cooling in conjunction with a so-called "dark" state whose transition to the excited state is not addressed by the resonant lasers. Ultracold atomic physics experiments on atomic species with poorly-resolved hyperfine structure, like isotopes of lithium and potassium, often utilize gray molasses instead of Sisyphus cooling as a secondary cooling stage after the ubiquitous magneto-optical trap (MOT) to achieve temperatures below the Doppler limit. Unlike a MOT, which combines a molasses force with a confining force, a gray molasses can only slow but not trap atoms; hence, its efficacy as a cooling mechanism lasts only milliseconds before further cooling and trapping stages must be employed.

In quantum physics, light is in a squeezed state if its electric field strength Ԑ for some phases has a quantum uncertainty smaller than that of a coherent state. The term squeezing thus refers to a reduced quantum uncertainty. To obey Heisenberg's uncertainty relation, a squeezed state must also have phases at which the electric field uncertainty is anti-squeezed, i.e. larger than that of a coherent state. Since 2019, the gravitational-wave observatories LIGO and Virgo employ squeezed laser light, which has significantly increased the rate of observed gravitational-wave events.

Quantum optical coherence tomography (Q-OCT) is an imaging technique that uses nonclassical (quantum) light sources to generate high-resolution images based on the Hong-Ou-Mandel effect (HOM). Q-OCT is similar to conventional OCT but uses a fourth-order interferometer that incorporates two photodetectors rather than a second-order interferometer with a single photodetector. The primary advantage of Q-OCT over OCT is insensitivity to even-order dispersion in multi-layered and scattering media.

References

  1. ↑ Lerch, Stefan; Bessire, Bänz; Bernhard, Christof; Feurer, Thomas; Stefanov, André (2013-04-01). "Tuning curve of type-0 spontaneous parametric down-conversion". Journal of the Optical Society of America B. 30 (4): 953–958. arXiv: 1404.1192 . Bibcode:2013JOSAB..30..953L. doi:10.1364/JOSAB.30.000953. ISSN   0740-3224. S2CID   149192.
  2. ↑ Boyd, Robert (2008). Nonlinear Optics, Third Edition . New York: Academic Press. pp.  79–88. ISBN   978-0-12-369470-6.
  3. ↑ Bock, Matthias; Lenhard, Andreas; Chunnilall, Christopher; Becher, Christoph (17 October 2016). "Highly efficient heralded single-photon source for telecom wavelengths based on a PPLN waveguide". Optics Express. 24 (21): 23992–24001. Bibcode:2016OExpr..2423992B. doi: 10.1364/OE.24.023992 . ISSN   1094-4087. PMID   27828232.
  4. ↑ P. Kwiat; et al. (1995). "New High-Intensity Source of Polarization-Entangled Photon Pairs". Phys. Rev. Lett. 75 (24): 4337–4341. Bibcode:1995PhRvL..75.4337K. doi: 10.1103/PhysRevLett.75.4337 . PMID   10059884.
  5. ↑ Anton Zeilinger (12 October 2010). "The super-source and closing the communication loophole". Dance of the Photons: From Einstein to Quantum Teleportation. Farrar, Straus and Giroux. ISBN   978-1-4299-6379-4.
  6. ↑ Reck, M H A, Quantum Interferometry with Multiports: Entangled Photons in Optical Fibers (page 115) (PDF), retrieved 16 February 2014
  7. ↑ Harris, S. E.; Oshman, M. K.; Byer, R. L. (1967-05-01). "Observation of Tunable Optical Parametric Fluorescence". Physical Review Letters. 18 (18): 732–734. doi:10.1103/PhysRevLett.18.732.
  8. ↑ Magde, Douglas; Mahr, Herbert (1967-05-22). "Study in Ammonium Dihydrogen Phosphate of Spontaneous Parametric Interaction Tunable from 4400 to 16 000 \AA{}". Physical Review Letters. 18 (21): 905–907. doi:10.1103/PhysRevLett.18.905.
  9. ↑ 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.
  10. ↑ Ghosh, R.; Mandel, L. (1987). "Observation of Nonclassical Effects in the Interference of Two Photons". Phys. Rev. Lett. 59 (17): 1903–1905. Bibcode:1987PhRvL..59.1903G. doi:10.1103/physrevlett.59.1903. PMID   10035364.
  11. ↑ http://pra.aps.org/abstract/PRA/v62/i4/e043816 - Duality between partial coherence and partial entanglement
  12. ↑ Zavatta, Alessandro; Viciani, Silvia; Bellini, Marco (2004). "Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection". Physical Review A. 70 (5): 053821. arXiv: quant-ph/0406090 . Bibcode:2004PhRvA..70e3821Z. doi:10.1103/PhysRevA.70.053821. S2CID   119387795.
  13. ↑ Walborn, S.P.; Monken, C.H.; Pádua, S.; Souto Ribeiro, P.H. (2010). "Spatial correlations in parametric down-conversion". Physics Reports. 495 (4–5): 87–139. arXiv: 1010.1236 . Bibcode:2010PhR...495...87W. doi:10.1016/j.physrep.2010.06.003. ISSN   0370-1573. S2CID   119221135.
  14. ↑ Hayat, Alex; Ginzburg, Pavel; Orenstein, Meir (2008-03-02). "Observation of two-photon emission from semiconductors". Nature Photonics. 2 (4). Springer Science and Business Media LLC: 238–241. doi:10.1038/nphoton.2008.28. ISSN   1749-4885.
  15. ↑ Chluba, J.; Sunyaev, R. A. (2006). "Induced two-photon decay of the 2s level and the rate of cosmological hydrogen recombination". Astronomy and Astrophysics. 446 (1): 39–42. arXiv: astro-ph/0508144 . Bibcode:2006A&A...446...39C. doi:10.1051/0004-6361:20053988. S2CID   119526307.
  16. ↑ Forbes, Kayn A.; Ford, Jack S.; Andrews, David L. (2017-03-30). "Nonlocalized Generation of Correlated Photon Pairs in Degenerate Down-Conversion" (PDF). Physical Review Letters. 118 (13): 133602. Bibcode:2017PhRvL.118m3602F. doi:10.1103/PhysRevLett.118.133602. PMID   28409956.
  17. ↑ Forbes, Kayn A.; Ford, Jack S.; Jones, Garth A.; Andrews, David L. (2017-08-23). "Quantum delocalization in photon-pair generation" (PDF). Physical Review A. 96 (2): 023850. Bibcode:2017PhRvA..96b3850F. doi:10.1103/PhysRevA.96.023850.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.