Optical parametric oscillator: Difference between revisions

Revision as of 10:00, 27 December 2024

Revision as of 03:47, 11 April 2025

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In the optical parametric oscillator the initial idler and signal waves are taken from background waves, which are always present. If the idler wave is given from the outside along with the pump beam, then the process is called [[difference frequency generation]] (DFG). This is a more efficient process than optical parametric oscillation, and in principle can be thresholdless.

In order to change the output wave frequencies, one can change the pump frequency or the [[Nonlinear Optics|phasematching]] properties of the nonlinear optical crystal. This latter is accomplished by changing its temperature or orientation or quasi-phasematching period (see below). For fine-tuning one can also change the [[optical path length]] of the resonator. In addition, the resonator may contain elements to suppress mode-hops of the resonating wave. This often requires active control of some element of the OPO system.

If the nonlinear optical crystal cannot be phase-matched, [[quasi-phase-matching]] (QPM) can be employed. This is accomplished by periodically changing the nonlinear optical properties of the crystal, mostly by [[periodical poling]]. With a suitable range of periods, output wavelengths from 700 nm to 5000 nm can be generated in periodically poled [[lithium niobate]] (PPLN). Common pump sources are [[Nd-YAG laser|neodymium lasers]] at 1064 nm or 532 nm.

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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|s2cid=30991384 }}</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|s2cid=2999038 }}</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 | journal = Phys. Rev. Lett. | volume = 104 | issue = 25| page = 251102 | doi = 10.1103/PhysRevLett.104.251102 | bibcode=2010PhRvL.104y1102E|arxiv = 1007.0574 | pmid=20867358| s2cid = 9929939 }}</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|s2cid=13815567 }}</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|s2cid=37328629 }}</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 = https://www.science.org/doi/abs/10.1126/science.1178683 | journal = Science | volume = 326 | issue = 5954| pages = 823–826 | doi=10.1126/science.1178683| pmid = 19762598 |arxiv = 1009.4250 |bibcode = 2009Sci...326..823C | s2cid = 29660274 }}</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|author3-link= Sara 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 |s2cid=119471952 }}</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 | journal = Phys. Rev. Lett. | volume = 88 | issue = 20| page = 203601 | doi = 10.1103/PhysRevLett.88.203601 | pmid = 12005563 | bibcode=2002PhRvL..88t3601T|arxiv = quant-ph/0204017 | s2cid = 20948903 }}</ref>

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