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|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 = |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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An important feature of the OPO is the coherence and the spectral width of the generated radiation.

When the pump power is significantly above threshold, the two output waves are, to a very good approximation, [[coherent state]]s (laser-like waves). The linewidth of the resonated wave is very narrow (as low as several kHz). The nonresonated generated wave also exhibits narrow linewidth if a pump wave of narrow linewidth is employed. Narrow-linewidth OPOs are widely used in spectroscopy.<ref name = BJO>{{cite book |editor =[[F. J. Duarte|Duarte FJ]] |title=Tunable Laser Applications | edition = 3rd |publisher= [[CRC Press]] |___location=Boca Raton |year=2016 |isbn=9781482261066 |oclc= |doi= |accessdate= | authors =[[Brian Orr|Orr BJ]], Haub JG, White RT | chapter = Spectroscopic Applications of Pulsed Tunable Optical Parametric Oscillators | pages = 17–142 }}</ref>

==Quantum properties of the generated light beams==

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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 |name-list-style=amp |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 |name-list-style=amp |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 |name-list-style=amp |journal=Phys. Rev. Lett. |volume=59|doi=10.1103/PhysRevLett.59.2555 |pmid=10035582 |year=1987|title=Observation of Quantum Noise Reduction on Twin Laser Beams|issue=22|pages=2555–2557 |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 |name-list-style=amp |journal=Phys. Rev. Lett. |volume=60|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 |name-list-style=amp |journal=Phys. Rev. Lett. |volume=68|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 |name-list-style=amp |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>

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It has been recently predicted that all three fields (pump, signal and idler) must be entangled,<ref>{{cite journal|author1=A. S. Villar |author2=M. Martinelli |author3=C Fabre |author4=P. Nussenzveig |name-list-style=amp |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 |pmid=17155232}}</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| pmid = 19762598 |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|author1=M. Martinelli |author2=N. Treps |author3=S. Ducci |author4=S. Gigan |author5=A. Maître |author6=C. Fabre |name-list-style=amp |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>

==Applications==