Optical parametric oscillator: Difference between revisions

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An '''optical parametric oscillator''' ('''OPO''') is a [[parametric oscillator]] that oscillates at optical frequencies. It converts an input [[laser]] wave (called "pump") with frequency <math>\omega_p</math> into two output waves of lower frequency (<math>\omega_s, \omega_i</math>) by means of second-[[Orders of approximation|order]] [[nonlinear optics|nonlinear optical interaction]]. The sum of the output waves' frequencies is equal to the input wave frequency: <math>\omega_s + \omega_i=\omega_p</math>. 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, <math>\omega_s=\omega_i=\omega_p/2</math>, which can result in [[half-harmonic generation]] when signal and idler have the same polarization.

The first optical parametric oscillator was demonstrated by Joseph A. Giordmaine and Robert C. Miller in 1965,<ref>{{Cite journal|url = http://link.aps.org/doi/10.1103/PhysRevLett.14.973|title = Tunable Coherent Parametric Oscillation in LiNbO3 at Optical Frequencies|last = Giordmaine|first = J.|journal = Phys. Rev. Lett.|doi = 10.1103/PhysRevLett.14.973|pmid = |access-date = |last2 = Miller|first2 = R.|publisher = APS|year = 1965|volume = 14|issue = 24|page = 973|bibcode = 1965PhRvL..14..973G }}</ref> five years after the invention of the laser, at Bell Labs. Optical parametric oscillators are used as coherent light sources for various scientific purposes, and to generate [[squeezed light]] for quantum mechanics research. A Soviet report was also published in 1965.<ref>Akhmanov SA, Kovrigin AI, Piskarskas AS, Fadeev VV, Khokhlov RV, Observation of parametric amplification in the optical range, JETP Letters 2, No.7, 191-193 (1965).</ref>

==Overview==

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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> 5{{cite journal|author1=J. Jing |author2=J. Zhang |author3=Y. Yan |author4=F. Zhao |author5=C. Xie |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 |pmid=12732011}}</ref><ref>{{cite journal|author1=N. Takei |author2=H. Yonezawa |author3=T. Aoki |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 |pmid=16090375}}</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|author1=A. Heidmann |author2=R. J. Horowicz |author3=S. Reynaud |author4=E. Giacobino |author5=C. Fabre |author6=G. Camy |last-author-amp=yes |journal=Phys. Rev. Lett. |volume=59|page=2555|doi=10.1103/PhysRevLett.59.2555 |pmid=10035582 |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&nbsp;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 | pmid=20867358}}</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|author1=M. D. Reid |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|pages=2731–2733 |bibcode=1988PhRvL..60.2731R |pmid=10038437}}</ref> Below threshold, entanglement was measured for the first time in 1992,<ref>{{cite journal|author1=Z. Y. Ou |author2=S. F. Pereira |author3=H. J. Kimble |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|pages=3663–3666 |bibcode=1992PhRvL..68.3663O |pmid=10045765|url=http://authors.library.caltech.edu/6493/1/OUZprl92.pdf}}</ref> and in 2005 above threshold.<ref>{{cite journal|author1=A. S. Villar |author2=L. S. Cruz |author3=K. N. Cassemiro |author4=M. Martinelli |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 |pmid=16384378}}</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 name="KasaiJiangrui1997">{{cite journal|last1=Kasai|first1=K|last2=Jiangrui|first2=Gao|last3=Fabre|first3=C|title=Observation of squeezing using cascaded nonlinearity|journal=Europhysics Letters (EPL)|volume=40|issue=1|year=1997|pages=25–30|issn=0295-5075|doi=10.1209/epl/i1997-00418-8|bibcode=1997EL.....40...25K|citeseerx=10.1.1.521.1373}}</ref>

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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|author1=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|issue=17|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|urlpmid=http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-20-17-1932223038574|arxiv = 1206.0815 |bibcode = 2012OExpr..2019322M }}</ref>

==See also==