## Tripartite entanglement generation via four-wave mixings: narrowband triphoton W state

JOSA B, Vol. 27, Issue 6, pp. A11-A20 (2010)

http://dx.doi.org/10.1364/JOSAB.27.000A11

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### Abstract

We propose a method to generate a narrowband triphoton W state entangled in time (or energy) via two four-wave mixing processes in cold atomic gas media. The calculation of such a triphoton W state is performed with second-order perturbation theory. To characterize the optical properties of the state, we analyze the two-photon and three-photon temporal correlations in the photon coincidence counting measurement. Considering the role of determining the time coherence of triphotons between the nonlinear susceptibilities and phase matchings, we concentrate on two regimes, damped Rabi oscillation and group delay, to look at the temporal correlations. To further enhance the nonlinear interactions, it may be promising to consider cold atoms confined within hollow fibers or loaded into a high-Q cavity.

© 2010 Optical Society of America

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Entanglement in Photonic Systems

**History**

Original Manuscript: August 3, 2009

Revised Manuscript: December 13, 2009

Manuscript Accepted: December 19, 2009

Published: February 9, 2010

**Citation**

Jianming Wen, Eun Oh, and Shengwang Du, "Tripartite entanglement generation via four-wave mixings: narrowband triphoton W state," J. Opt. Soc. Am. B **27**, A11-A20 (2010)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-6-A11

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### References

- D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell's theorem,” in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Kafatos, ed. (Kluwer, 1989).
- A. Zeilinger, M. A. Horne, and D. M. Greenberger, NASA Conf. Publ. No. 3135 (National Aeronautics and Space Administration, Code NTT, Washington D.C., 1997).
- W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000). [CrossRef]
- A. Cabello, “Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states,” Phys. Rev. A 65, 032108 (2002). [CrossRef]
- D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999). [CrossRef]
- J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000). [CrossRef] [PubMed]
- M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004). [CrossRef] [PubMed]
- C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004). [CrossRef] [PubMed]
- H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, “New high-efficiency source of a three-photon W state and its full characterization using quantum state tomography,” Phys. Rev. Lett. 95, 150404 (2005). [CrossRef] [PubMed]
- Y.-A. Chen, T. Yang, A.-N. Zhang, Z. Zhao, A. Cabello, and J.-W. Pan, “Experimental violation of Bell's inequality beyond Tsirelson's bound,” Phys. Rev. Lett. 97, 170408 (2006). [CrossRef] [PubMed]
- L. K. Shalm, R. B. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457, 67-70 (2009). [CrossRef] [PubMed]
- J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009). [CrossRef]
- P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482-3485 (2000). [CrossRef] [PubMed]
- P. Van Loock and S. L. Braunstein, “Greenberger-Horne-Zeilinger nonlocality in phase space,” Phys. Rev. A 63, 022106 (2001). [CrossRef]
- G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001). [CrossRef]
- J.-M. Wen and M. H. Rubin, “Distinction of tripartite Greenberger-Horne-Zeilinger and W states entangled in time (or energy) and space,” Phys. Rev. A 79, 025802 (2009). [CrossRef]
- J.-M. Wen, P. Xu, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in tripartite entanglement: Geometrical and physical optics,” Phys. Rev. A 76, 023828 (2007). [CrossRef]
- J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Spatial resolution enhancement in quantum imaging beyond the diffraction limit using entangled photon-number state,” ArXiv:0812.2032.
- L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413-418 (2001). [CrossRef] [PubMed]
- Y.-H. Shih, “Entangled biphoton source—property and preparation,” Rep. Prog. Phys. 66, 1009-1044 (2003). [CrossRef]
- Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83, 2556-2559 (1999). [CrossRef]
- H. Wang, T. Horikiri, and T. Kobayashi, “Polarization-entangled mode-locked photons from cavity-enhanced spontaneous parametric down-conversion,” Phys. Rev. A 70, 043804 (2004). [CrossRef]
- C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97, 223601 (2006). [CrossRef] [PubMed]
- J. S. Neergaard-Nielsen, B. M. Nielsen, H. Takahashi, A. I. Vistnes, and E. S. Polzik, “High purity bright single photon source,” Opt. Express 15, 7940-7949 (2007). [CrossRef] [PubMed]
- J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. I. Perturbation theory,” Phys. Rev. A 74, 023808 (2006). [CrossRef]
- J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. II. Beyond perturbation theory,” Phys. Rev. A 74, 023809 (2006). [CrossRef]
- J.-M. Wen, S. Du, and M. H. Rubin, “Biphoton generation in a two-level atomic ensemble,” Phys. Rev. A 75, 033809 (2007). [CrossRef]
- J.-M. Wen, S. Du, and M. H. Rubin, “Spontaneous parametric down-conversion in a three-level system,” Phys. Rev. A 76, 013825 (2007). [CrossRef]
- J.-M. Wen, S. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008). [CrossRef]
- P. Kolchin, “Electromagnetically-induced-transparency-based paired photon generation,” Phys. Rev. A 75, 033814 (2007). [CrossRef]
- C. H. R. Ooi and M. O. Scully, “Two-photon correlation in a cascade amplifier: Propagation effects via a simple model, nonclassical regimes, and validity of neglecting Langevin noise,” Phys. Rev. A 76, 043822 (2007). [CrossRef]
- S. Du, J.-M. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B 25, C98-C108 (2008). [CrossRef]
- C. I. Osorio, S. Barreiro, M. W. Mitchell, and J. P. Torres, “Spatial entanglement of paired photons generated in cold atomic ensembles,” Phys. Rev. A 78, 052301 (2008). [CrossRef]
- Y. P. Huang and M. G. Moore, “Ultra-bright biphoton emission from an atomic vapor based on Doppler-free four-wave-mixing and collective emission,” arXiv:0901.4789.
- V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94, 183601 (2005). [CrossRef] [PubMed]
- P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: Use of a single driving laser,” Phys. Rev. Lett. 97, 113602 (2006). [CrossRef] [PubMed]
- S. Du, J.-M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007). [CrossRef] [PubMed]
- S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008). [CrossRef] [PubMed]
- H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999). [CrossRef]
- S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36-41 (1997). [CrossRef]
- M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633-673 (2005). [CrossRef]
- M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, “Spectral properties of three-photon entangled states generated via three-photon parametric down-conversion in a χ(3) medium,” Phys. Rev. A 72, 023818 (2005). [CrossRef]
- T. E. Keller, M. H. Rubin, Y.-H. Shih, and L.-A. Wu, “Theory of the three-photon entangled state,” Phys. Rev. A 57, 2076-2079 (1998). [CrossRef]
- M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009). [CrossRef] [PubMed]
- J. K. Thompson, J. Simon, H. Loh, and V. Vuletic, “A high-brightness source of narrowband, identical-photon pairs,” Science 313, 74-77 (2006). [CrossRef] [PubMed]
- M. H. Rubin, D. N. Klyshko, Y.-H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122-5133 (1994). [CrossRef] [PubMed]
- D. N. Klyshko, Photons and Nonlinear Optics (Gordon and Breach, 1988).
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).
- M. D. Lukin, P. R. Hemmer, and M. O. Scully, “Resonant nonlinear optics in phase-coherent media,” in Adv. At., Mol., Opt. Phys. Vol. 42, B.Bederson and H.Walther, eds. (Elsevier, 2000), pp. 347-386.
- M. H. Rubin, “Transverse correlation in optical spontaneous parametric down-conversion,” Phys. Rev. A 54, 5349-5360 (1996). [CrossRef] [PubMed]
- L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
- S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149-2151 (2008). [CrossRef] [PubMed]
- J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in multiphoton entanglement,” Phys. Rev. A 76, 045802 (2007). [CrossRef]
- Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007). [CrossRef] [PubMed]
- Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009). [CrossRef] [PubMed]

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