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==Quantum properties of the generated light beams==
[[File:OPO Crystals.jpg|thumb|300 px|right|[[Potassium titanyl phosphate|KTP]] crystals in an OPO]]
The OPO is the physical system most widely used to generate [[squeezed coherent states]] and [[Quantum entanglement|entangled]] states of light in the continuous variables regime. Many demonstrations of quantum information protocols for continuous variables were realized using OPOs.<ref>{{cite journal|authorauthor1=J. Jing, |author2=J. Zhang, |author3=Y. Yan, |author4=F. Zhao, |author5=C. Xie, and |author6=K. Peng |last-author-amp=yes |journal=Phys. Rev. Lett. |volume=90|page=167903|doi=10.1103/PhysRevLett.90.167903 |year=2003|title=Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables|issue=16|bibcode=2003PhRvL..90p7903J|arxiv = quant-ph/0210132 }}</ref><ref>{{cite journal|authorauthor1=N. Takei, |author2=H. Yonezawa, |author3=T. Aoki, and |author4=A. Furusawa |last-author-amp=yes |journal=Phys. Rev. Lett. |volume=94|page=220502|doi=10.1103/PhysRevLett.94.220502 |year=2005|title=High-Fidelity Teleportation beyond the No-Cloning Limit and Entanglement Swapping for Continuous Variables|issue=22|bibcode=2005PhRvL..94v0502T|arxiv = quant-ph/0501086 }}</ref>
The [[Spontaneous parametric down conversion|downconversion]] process really occurs in the single photon regime: each pump photon that is annihilated inside the cavity gives rise to a pair of photons in the signal and idler intracavity modes. This leads to a quantum correlation between the intensities of signal and idler fields, so that there is squeezing in the subtraction of intensities,<ref>{{cite journal|authorauthor1=A. Heidmann, |author2=R. J. Horowicz, |author3=S. Reynaud, |author4=E. Giacobino, |author5=C. Fabre, and |author6=G. Camy |last-author-amp=yes |journal=Phys. Rev. Lett. |volume=59|page=2555|doi=10.1103/PhysRevLett.59.2555 |year=1987|title=Observation of Quantum Noise Reduction on Twin Laser Beams|issue=22|bibcode=1987PhRvL..59.2555H}}</ref> which motivated the name "twin beams" for the downconverted fields. The highest squeezing level attained to date is 12.7 dB.<ref>{{cite journal | last1 = Eberle | first1 = T. | last2 = Steinlechner | first2 = S. | last3 = Bauchrowitz | first3 = J. | last4 = Händchen | first4 = V. | last5 = Vahlbruch | first5 = H. | last6 = Mehmet | first6 = M. | last7 = Müller-Ebhardt | first7 = H. | last8 = Schnabel | first8 = R. | year = 2010 | title = Quantum Enhancement of the Zero-Area Sagnac Interferometer Topology for Gravitational Wave Detection | url = | journal = Phys. Rev. Lett | volume = 104 | issue = 25| page = 251102 | doi = 10.1103/PhysRevLett.104.251102 | bibcode=2010PhRvL.104y1102E|arxiv = 1007.0574 }}</ref>
It turns out that the phases of the twin beams are quantum correlated as well, leading to [[Quantum entanglement|entanglement]], theoretically predicted in 1988.<ref>{{cite journal|authorauthor1=M. D. Reid and |author2=P. D. Drummond |lastauthoramp=yes |journal=Phys. Rev. Lett. |volume=60|page=2731|doi=10.1103/PhysRevLett.60.2731 |year=1988|title=Quantum Correlations of Phase in Nondegenerate Parametric Oscillation|issue=26|bibcode=1988PhRvL..60.2731R}}</ref> Below threshold, entanglement was measured for the first time in 1992,<ref>{{cite journal|authorauthor1=Z. Y. Ou, |author2=S. F. Pereira, |author3=H. J. Kimble, and |author4=K. C. Peng |last-author-amp=yes |journal=Phys. Rev. Lett. |volume=68|page=3663|doi=10.1103/PhysRevLett.68.3663 |year=1992|title=Realization of the Einstein-Podolsky-Rosen paradox for continuous variables|issue=25|bibcode=1992PhRvL..68.3663O}}</ref> and in 2005 above threshold.<ref>{{cite journal|authorauthor1=A. S. Villar, |author2=L. S. Cruz, |author3=K. N. Cassemiro, |author4=M. Martinelli, and |author5=P. Nussenzveig |last-author-amp=yes |journal=Phys. Rev. Lett. |volume=95|page=243603|doi=10.1103/PhysRevLett.95.243603 |year=2005|title=Generation of Bright Two-Color Continuous Variable Entanglement|issue=24|bibcode=2005PhRvL..95x3603V|arxiv = quant-ph/0506139 }}</ref>
Above threshold, the pump beam depletion makes it sensitive to the quantum phenomena happening inside the crystal. The first measurement of squeezing in the pump field after parametric interaction was done in 1997.<ref>{{cite journal|authorauthor1=K. Kasai, |author2=J.G. Gao, and |author3=C. Fabre |last-author-amp=yes |journal= Europhys. Lett.|volume=40|page=25 |year=1997|bibcode = 1997EL.....40...25K |doi = 10.1209/epl/i1997-00418-8 }}</ref> It has been recently predicted that all three fields (pump, signal and idler) must be entangled,<ref>{{cite journal|authorauthor1=A. S. Villar, |author2=M. Martinelli, |author3=C Fabre, and |author4=P. Nussenzveig |last-author-amp=yes |journal=Phys. Rev. Lett. |volume=97|page=140504|doi=10.1103/PhysRevLett.97.140504 |year=2006|title=Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold Optical Parametric Oscillator|issue=14|bibcode=2006PhRvL..97n0504V|arxiv = quant-ph/0610062 }}</ref> a prediction which was experimentally demonstrated by the same group.<ref>{{cite journal | last1 = Coelho | first1 = A. S. | last2 = Barbosa | first2 = F. A. S. | last3 = Cassemiro | first3 = K. N. | last4 = Villar | first4 = A. S. | last5 = Martinelli | first5 = M. | last6 = Nussenzveig | first6 = P. | year = 2009 | title = Three-Color Entanglement | url = http://www.sciencemag.org/content/326/5954/823.abstract | journal = Science | volume = 326 | issue = 5954| pages = 823–826 | doi=10.1126/science.1178683|arxiv = 1009.4250 |bibcode = 2009Sci...326..823C }}</ref>
Not only intensity and phase of the twin beams share quantum correlations, but also do their spatial modes.<ref>{{cite journal|authorauthor1=M. Martinelli, |author2=N. Treps, |author3=S. Ducci, |author4=S. Gigan, |author5=A. Maître, and |author6=C. Fabre |last-author-amp=yes |journal=Phys. Rev. A |volume=67|page=023808|doi=10.1103/PhysRevA.67.023808 |year=2003|title=Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator|issue=2|arxiv = quant-ph/0210023 |bibcode = 2003PhRvA..67b3808M }}</ref> This feature could be used to enhance signal to noise ratio in image systems and hence surpass the standard quantum limit (or the shot noise limit) for imaging.<ref>{{cite journal | last1 = Treps | first1 = N. | last2 = Andersen | first2 = U. | last3 = Buchler | first3 = B. | last4 = Lam | first4 = P. K. | last5 = Maitre | first5 = A. | last6 = Bachor | first6 = H.-A. | last7 = Fabre | first7 = C. | year = 2002 | title = Surpassing the Standard Quantum Limit for Optical Imaging Using Nonclassical Multimode Light | url = | journal = Phys. Rev. Lett | volume = 88 | issue = 20| page = 203601 | doi = 10.1103/PhysRevLett.88.203601 | bibcode=2002PhRvL..88t3601T|arxiv = quant-ph/0204017 }}</ref>
The OPO is being employed nowadays as a source of squeezed light tuned to atomic transitions, in order to study how the atoms interact with squeezed light.<ref>{{cite journal|authorauthor1=T. Tanimura, |author2=D. Akamatsu, |author3=Y. Yokoi, |author4=A. Furusawa, |author5=M. Kozuma |journal=Opt. Lett. |volume=31|pages=2344–6|doi=10.1364/OL.31.002344 |year=2006|title=Generation of a squeezed vacuum resonant on a rubidium D1 line with periodically poled KTiOPO4|issue=15|pmid=16832480|arxiv = quant-ph/0603214 |bibcode = 2006OptL...31.2344T }}</ref>
It is also recently demonstrated that a degenerate OPO can be used as an all-optical quantum [[Hardware random number generator|random number generator]] that does not require post processing.<ref>{{cite journal|last=Marandi|first=A.|author2=N. C. Leindecker |author3=K. L. Vodopyanov |author4=R. L. Byer |journal=Opt. Express|volume=20|pages= 19322–19330|year=2012|title=All-optical quantum random bit generation from intrinsically binary phase of parametric oscillators|doi=10.1364/OE.20.019322|url=http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-20-17-19322|arxiv = 1206.0815 |bibcode = 2012OExpr..2019322M }}</ref>
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