Abstract

We experimentally investigated the intensity cross-correlation between the upconverted photons and the unconverted photons in the single-photon frequency upconversion process with multi-longitudinal mode pump and signal sources. In theoretical analysis, with this multi-longitudinal mode of both signal and pump sources system, the properties of the signal photons could also be maintained as in the single-mode frequency upconversion system. Experimentally, based on the conversion efficiency of 80.5%, the joint probability of simultaneously detecting at upconverted and unconverted photons showed an anti-correlation as a function of conversion efficiency which indicated the upconverted photons were one-to-one from the signal photons. While due to the coherent state of the signal photons, the intensity cross-correlation function g(2)(0) was shown to be equal to unity at any conversion efficiency, agreeing with the theoretical prediction. This study will benefit the high-speed wavelength-tunable quantum state translation or photonic quantum interface together with the mature frequency tuning or longitudinal mode selection techniques.

© 2012 OSA

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  1. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
    [CrossRef] [PubMed]
  2. D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
    [CrossRef]
  3. S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437(7055), 116–120 (2005).
    [CrossRef] [PubMed]
  4. P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81(2), 021801 (2010).
    [CrossRef]
  5. S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
    [CrossRef]
  6. A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-IIPPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010).
    [CrossRef]
  7. K. P. Petrov, S. Waltman, E. J. Dlugokencky, M. Arbore, M. M. Fejer, F. K. Tittel, and L. W. Hollberg, “Precise measurement of methane in air using diode-pumped 3.4-μm difference-frequency generation in PPLN,” Appl. Phys. B 64, 567–572 (1997).
    [CrossRef]
  8. H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70(3), 031802 (2004).
    [CrossRef]
  9. Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75(2), 023803 (2007).
    [CrossRef]
  10. H. Takesue, “Erasing distinguishability using quantum frequency up-conversion,” Phys. Rev. Lett. 101(17), 173901 (2008).
    [CrossRef] [PubMed]
  11. J. Chen, F. K. Lee, X. Li, L. P. Voss, and P. Kumar, “Schemes for fiber-based entanglement generation in the telecom band,” New J. Phys. 9(8), 289 (2007).
    [CrossRef]
  12. J. Chen, J. B. Altepeter, and P. Kumar, “Quantum-state engineering using nonlinear optical Sangac loops,” New J. Phys. 10(12), 123019 (2008).
    [CrossRef]
  13. M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
    [CrossRef]
  14. M. A. Albota and F. N. C. Wong, “Efficient single-photon counting at 1.55 microm by means of frequency upconversion,” Opt. Lett. 29(13), 1449–1451 (2004).
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  15. R. V. Roussev, C. Langrock, J. R. Kurz, and M. M. Fejer, “Periodically poled lithium niobate waveguide sum-frequency generator for efficient single-photon detection at communication wavelengths,” Opt. Lett. 29, 1518–1520 (2004).
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  16. H. Pan and H. Zeng, “Efficient and stable single-photon counting at 1.55 microm by intracavity frequency upconversion,” Opt. Lett. 31(6), 793–795 (2006).
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  17. J. M. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153–2156 (1992).
    [CrossRef] [PubMed]
  18. H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fiber,” New J. Phys. 7, 232 (2005).
    [CrossRef]
  19. R. T. Thew, H. Zbinden, and N. Gisin, “Tunable upconversion photon detector,” Appl. Phys. Lett. 93(7), 071104 (2008).
    [CrossRef]
  20. L. Ma, O. Slattery, and X. Tang, “Experimental study of high sensitivity infrared spectrometer with waveguide-based up-conversion detector(1),” Opt. Express 17(16), 14395–14404 (2009).
    [CrossRef] [PubMed]
  21. E. Pomarico, B. Sanguinetti, R. Thew, and H. Zbinden, “Room temperature photon number resolving detector for infared wavelengths,” Opt. Express 18(10), 10750–10759 (2010).
    [CrossRef] [PubMed]
  22. K. Huang, X. Gu, M. Ren, Y. Jian, H. Pan, G. Wu, E. Wu, and H. Zeng, “Photon-number-resolving detection at 1.04 μm via coincidence frequency upconversion,” Opt. Lett. 36(9), 1722–1724 (2011).
    [CrossRef] [PubMed]
  23. X. Gu, Y. Li, H. Pan, E. Wu, and H. Zeng, “High-speed single-photon frequency upconversion with synchronous pump pulses,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1748–1752 (2009).
    [CrossRef]
  24. X. Gu, K. Huang, Y. Li, H. Pan, E. Wu, and H. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010).
    [CrossRef]
  25. P. Kumar, “Quantum frequency conversion,” Opt. Lett. 15(24), 1476–1478 (1990).
    [CrossRef] [PubMed]
  26. H. Pan, E. Wu, H. Dong, and H. Zeng, “Single-photon frequency up-conversion with multimode pumping,” Phys. Rev. A 77(3), 033815 (2008).
    [CrossRef]
  27. A. Beveratos, S. Kühn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18(2), 191–196 (2002).
    [CrossRef]

2011 (1)

2010 (5)

X. Gu, K. Huang, Y. Li, H. Pan, E. Wu, and H. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010).
[CrossRef]

E. Pomarico, B. Sanguinetti, R. Thew, and H. Zbinden, “Room temperature photon number resolving detector for infared wavelengths,” Opt. Express 18(10), 10750–10759 (2010).
[CrossRef] [PubMed]

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81(2), 021801 (2010).
[CrossRef]

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-IIPPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010).
[CrossRef]

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

2009 (2)

L. Ma, O. Slattery, and X. Tang, “Experimental study of high sensitivity infrared spectrometer with waveguide-based up-conversion detector(1),” Opt. Express 17(16), 14395–14404 (2009).
[CrossRef] [PubMed]

X. Gu, Y. Li, H. Pan, E. Wu, and H. Zeng, “High-speed single-photon frequency upconversion with synchronous pump pulses,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1748–1752 (2009).
[CrossRef]

2008 (4)

R. T. Thew, H. Zbinden, and N. Gisin, “Tunable upconversion photon detector,” Appl. Phys. Lett. 93(7), 071104 (2008).
[CrossRef]

H. Pan, E. Wu, H. Dong, and H. Zeng, “Single-photon frequency up-conversion with multimode pumping,” Phys. Rev. A 77(3), 033815 (2008).
[CrossRef]

H. Takesue, “Erasing distinguishability using quantum frequency up-conversion,” Phys. Rev. Lett. 101(17), 173901 (2008).
[CrossRef] [PubMed]

J. Chen, J. B. Altepeter, and P. Kumar, “Quantum-state engineering using nonlinear optical Sangac loops,” New J. Phys. 10(12), 123019 (2008).
[CrossRef]

2007 (2)

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75(2), 023803 (2007).
[CrossRef]

J. Chen, F. K. Lee, X. Li, L. P. Voss, and P. Kumar, “Schemes for fiber-based entanglement generation in the telecom band,” New J. Phys. 9(8), 289 (2007).
[CrossRef]

2006 (1)

2005 (2)

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437(7055), 116–120 (2005).
[CrossRef] [PubMed]

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fiber,” New J. Phys. 7, 232 (2005).
[CrossRef]

2004 (3)

2002 (2)

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
[CrossRef]

A. Beveratos, S. Kühn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18(2), 191–196 (2002).
[CrossRef]

1997 (2)

D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[CrossRef]

K. P. Petrov, S. Waltman, E. J. Dlugokencky, M. Arbore, M. M. Fejer, F. K. Tittel, and L. W. Hollberg, “Precise measurement of methane in air using diode-pumped 3.4-μm difference-frequency generation in PPLN,” Appl. Phys. B 64, 567–572 (1997).
[CrossRef]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

1992 (1)

J. M. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153–2156 (1992).
[CrossRef] [PubMed]

1990 (1)

Aboussouan, P.

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81(2), 021801 (2010).
[CrossRef]

Agrawal, G. P.

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75(2), 023803 (2007).
[CrossRef]

Albota, M. A.

Alibart, O.

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-IIPPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010).
[CrossRef]

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81(2), 021801 (2010).
[CrossRef]

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437(7055), 116–120 (2005).
[CrossRef] [PubMed]

Altepeter, J. B.

J. Chen, J. B. Altepeter, and P. Kumar, “Quantum-state engineering using nonlinear optical Sangac loops,” New J. Phys. 10(12), 123019 (2008).
[CrossRef]

Arbore, M.

K. P. Petrov, S. Waltman, E. J. Dlugokencky, M. Arbore, M. M. Fejer, F. K. Tittel, and L. W. Hollberg, “Precise measurement of methane in air using diode-pumped 3.4-μm difference-frequency generation in PPLN,” Appl. Phys. B 64, 567–572 (1997).
[CrossRef]

Baldi, P.

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81(2), 021801 (2010).
[CrossRef]

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437(7055), 116–120 (2005).
[CrossRef] [PubMed]

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
[CrossRef]

Beveratos, A.

A. Beveratos, S. Kühn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18(2), 191–196 (2002).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[CrossRef]

Brouri, R.

A. Beveratos, S. Kühn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18(2), 191–196 (2002).
[CrossRef]

Chen, J.

J. Chen, J. B. Altepeter, and P. Kumar, “Quantum-state engineering using nonlinear optical Sangac loops,” New J. Phys. 10(12), 123019 (2008).
[CrossRef]

J. Chen, F. K. Lee, X. Li, L. P. Voss, and P. Kumar, “Schemes for fiber-based entanglement generation in the telecom band,” New J. Phys. 9(8), 289 (2007).
[CrossRef]

De Micheli, M.

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
[CrossRef]

De Riedmatten, H.

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
[CrossRef]

Diamanti, E.

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fiber,” New J. Phys. 7, 232 (2005).
[CrossRef]

Dlugokencky, E. J.

K. P. Petrov, S. Waltman, E. J. Dlugokencky, M. Arbore, M. M. Fejer, F. K. Tittel, and L. W. Hollberg, “Precise measurement of methane in air using diode-pumped 3.4-μm difference-frequency generation in PPLN,” Appl. Phys. B 64, 567–572 (1997).
[CrossRef]

Dong, H.

H. Pan, E. Wu, H. Dong, and H. Zeng, “Single-photon frequency up-conversion with multimode pumping,” Phys. Rev. A 77(3), 033815 (2008).
[CrossRef]

Eibl, M.

D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[CrossRef]

Fejer, M. M.

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fiber,” New J. Phys. 7, 232 (2005).
[CrossRef]

R. V. Roussev, C. Langrock, J. R. Kurz, and M. M. Fejer, “Periodically poled lithium niobate waveguide sum-frequency generator for efficient single-photon detection at communication wavelengths,” Opt. Lett. 29, 1518–1520 (2004).
[CrossRef] [PubMed]

K. P. Petrov, S. Waltman, E. J. Dlugokencky, M. Arbore, M. M. Fejer, F. K. Tittel, and L. W. Hollberg, “Precise measurement of methane in air using diode-pumped 3.4-μm difference-frequency generation in PPLN,” Appl. Phys. B 64, 567–572 (1997).
[CrossRef]

Gacoin, T.

A. Beveratos, S. Kühn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18(2), 191–196 (2002).
[CrossRef]

Gisin, N.

R. T. Thew, H. Zbinden, and N. Gisin, “Tunable upconversion photon detector,” Appl. Phys. Lett. 93(7), 071104 (2008).
[CrossRef]

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437(7055), 116–120 (2005).
[CrossRef] [PubMed]

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
[CrossRef]

Grangier, P.

A. Beveratos, S. Kühn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18(2), 191–196 (2002).
[CrossRef]

Gu, X.

K. Huang, X. Gu, M. Ren, Y. Jian, H. Pan, G. Wu, E. Wu, and H. Zeng, “Photon-number-resolving detection at 1.04 μm via coincidence frequency upconversion,” Opt. Lett. 36(9), 1722–1724 (2011).
[CrossRef] [PubMed]

X. Gu, K. Huang, Y. Li, H. Pan, E. Wu, and H. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010).
[CrossRef]

X. Gu, Y. Li, H. Pan, E. Wu, and H. Zeng, “High-speed single-photon frequency upconversion with synchronous pump pulses,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1748–1752 (2009).
[CrossRef]

Halder, M.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437(7055), 116–120 (2005).
[CrossRef] [PubMed]

Herrmann, H.

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-IIPPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010).
[CrossRef]

Hollberg, L. W.

K. P. Petrov, S. Waltman, E. J. Dlugokencky, M. Arbore, M. M. Fejer, F. K. Tittel, and L. W. Hollberg, “Precise measurement of methane in air using diode-pumped 3.4-μm difference-frequency generation in PPLN,” Appl. Phys. B 64, 567–572 (1997).
[CrossRef]

Honjo, T.

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fiber,” New J. Phys. 7, 232 (2005).
[CrossRef]

Huang, J. M.

J. M. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153–2156 (1992).
[CrossRef] [PubMed]

Huang, K.

K. Huang, X. Gu, M. Ren, Y. Jian, H. Pan, G. Wu, E. Wu, and H. Zeng, “Photon-number-resolving detection at 1.04 μm via coincidence frequency upconversion,” Opt. Lett. 36(9), 1722–1724 (2011).
[CrossRef] [PubMed]

X. Gu, K. Huang, Y. Li, H. Pan, E. Wu, and H. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010).
[CrossRef]

Inoue, K.

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fiber,” New J. Phys. 7, 232 (2005).
[CrossRef]

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70(3), 031802 (2004).
[CrossRef]

Issautier, A.

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-IIPPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010).
[CrossRef]

Jian, Y.

Kühn, S.

A. Beveratos, S. Kühn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18(2), 191–196 (2002).
[CrossRef]

Kumar, P.

J. Chen, J. B. Altepeter, and P. Kumar, “Quantum-state engineering using nonlinear optical Sangac loops,” New J. Phys. 10(12), 123019 (2008).
[CrossRef]

J. Chen, F. K. Lee, X. Li, L. P. Voss, and P. Kumar, “Schemes for fiber-based entanglement generation in the telecom band,” New J. Phys. 9(8), 289 (2007).
[CrossRef]

J. M. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153–2156 (1992).
[CrossRef] [PubMed]

P. Kumar, “Quantum frequency conversion,” Opt. Lett. 15(24), 1476–1478 (1990).
[CrossRef] [PubMed]

Kurz, J. R.

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Langrock, C.

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fiber,” New J. Phys. 7, 232 (2005).
[CrossRef]

R. V. Roussev, C. Langrock, J. R. Kurz, and M. M. Fejer, “Periodically poled lithium niobate waveguide sum-frequency generator for efficient single-photon detection at communication wavelengths,” Opt. Lett. 29, 1518–1520 (2004).
[CrossRef] [PubMed]

Lee, F. K.

J. Chen, F. K. Lee, X. Li, L. P. Voss, and P. Kumar, “Schemes for fiber-based entanglement generation in the telecom band,” New J. Phys. 9(8), 289 (2007).
[CrossRef]

Li, X.

J. Chen, F. K. Lee, X. Li, L. P. Voss, and P. Kumar, “Schemes for fiber-based entanglement generation in the telecom band,” New J. Phys. 9(8), 289 (2007).
[CrossRef]

Li, Y.

X. Gu, K. Huang, Y. Li, H. Pan, E. Wu, and H. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010).
[CrossRef]

X. Gu, Y. Li, H. Pan, E. Wu, and H. Zeng, “High-speed single-photon frequency upconversion with synchronous pump pulses,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1748–1752 (2009).
[CrossRef]

Lin, Q.

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75(2), 023803 (2007).
[CrossRef]

Ma, L.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

L. Ma, O. Slattery, and X. Tang, “Experimental study of high sensitivity infrared spectrometer with waveguide-based up-conversion detector(1),” Opt. Express 17(16), 14395–14404 (2009).
[CrossRef] [PubMed]

Martin, A.

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-IIPPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010).
[CrossRef]

Mattle, K.

D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Ostrowsky, D. B.

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81(2), 021801 (2010).
[CrossRef]

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-IIPPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010).
[CrossRef]

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
[CrossRef]

Pan, H.

K. Huang, X. Gu, M. Ren, Y. Jian, H. Pan, G. Wu, E. Wu, and H. Zeng, “Photon-number-resolving detection at 1.04 μm via coincidence frequency upconversion,” Opt. Lett. 36(9), 1722–1724 (2011).
[CrossRef] [PubMed]

X. Gu, K. Huang, Y. Li, H. Pan, E. Wu, and H. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010).
[CrossRef]

X. Gu, Y. Li, H. Pan, E. Wu, and H. Zeng, “High-speed single-photon frequency upconversion with synchronous pump pulses,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1748–1752 (2009).
[CrossRef]

H. Pan, E. Wu, H. Dong, and H. Zeng, “Single-photon frequency up-conversion with multimode pumping,” Phys. Rev. A 77(3), 033815 (2008).
[CrossRef]

H. Pan and H. Zeng, “Efficient and stable single-photon counting at 1.55 microm by intracavity frequency upconversion,” Opt. Lett. 31(6), 793–795 (2006).
[CrossRef] [PubMed]

Pan, J.

D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[CrossRef]

Petrov, K. P.

K. P. Petrov, S. Waltman, E. J. Dlugokencky, M. Arbore, M. M. Fejer, F. K. Tittel, and L. W. Hollberg, “Precise measurement of methane in air using diode-pumped 3.4-μm difference-frequency generation in PPLN,” Appl. Phys. B 64, 567–572 (1997).
[CrossRef]

Poizat, J. P.

A. Beveratos, S. Kühn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18(2), 191–196 (2002).
[CrossRef]

Pomarico, E.

Rakher, M. T.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

Ren, M.

Roussev, R. V.

Sanguinetti, B.

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Slattery, O.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

L. Ma, O. Slattery, and X. Tang, “Experimental study of high sensitivity infrared spectrometer with waveguide-based up-conversion detector(1),” Opt. Express 17(16), 14395–14404 (2009).
[CrossRef] [PubMed]

Sohler, W.

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-IIPPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010).
[CrossRef]

Srinivasan, K.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

Takesue, H.

H. Takesue, “Erasing distinguishability using quantum frequency up-conversion,” Phys. Rev. Lett. 101(17), 173901 (2008).
[CrossRef] [PubMed]

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fiber,” New J. Phys. 7, 232 (2005).
[CrossRef]

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70(3), 031802 (2004).
[CrossRef]

Tang, X.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

L. Ma, O. Slattery, and X. Tang, “Experimental study of high sensitivity infrared spectrometer with waveguide-based up-conversion detector(1),” Opt. Express 17(16), 14395–14404 (2009).
[CrossRef] [PubMed]

Tanzilli, S.

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-IIPPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010).
[CrossRef]

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81(2), 021801 (2010).
[CrossRef]

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437(7055), 116–120 (2005).
[CrossRef] [PubMed]

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
[CrossRef]

Thew, R.

Thew, R. T.

R. T. Thew, H. Zbinden, and N. Gisin, “Tunable upconversion photon detector,” Appl. Phys. Lett. 93(7), 071104 (2008).
[CrossRef]

Tittel, F. K.

K. P. Petrov, S. Waltman, E. J. Dlugokencky, M. Arbore, M. M. Fejer, F. K. Tittel, and L. W. Hollberg, “Precise measurement of methane in air using diode-pumped 3.4-μm difference-frequency generation in PPLN,” Appl. Phys. B 64, 567–572 (1997).
[CrossRef]

Tittel, W.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437(7055), 116–120 (2005).
[CrossRef] [PubMed]

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
[CrossRef]

Voss, L. P.

J. Chen, F. K. Lee, X. Li, L. P. Voss, and P. Kumar, “Schemes for fiber-based entanglement generation in the telecom band,” New J. Phys. 9(8), 289 (2007).
[CrossRef]

Waltman, S.

K. P. Petrov, S. Waltman, E. J. Dlugokencky, M. Arbore, M. M. Fejer, F. K. Tittel, and L. W. Hollberg, “Precise measurement of methane in air using diode-pumped 3.4-μm difference-frequency generation in PPLN,” Appl. Phys. B 64, 567–572 (1997).
[CrossRef]

Weinfurter, H.

D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Wong, F. N. C.

Wu, E.

K. Huang, X. Gu, M. Ren, Y. Jian, H. Pan, G. Wu, E. Wu, and H. Zeng, “Photon-number-resolving detection at 1.04 μm via coincidence frequency upconversion,” Opt. Lett. 36(9), 1722–1724 (2011).
[CrossRef] [PubMed]

X. Gu, K. Huang, Y. Li, H. Pan, E. Wu, and H. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010).
[CrossRef]

X. Gu, Y. Li, H. Pan, E. Wu, and H. Zeng, “High-speed single-photon frequency upconversion with synchronous pump pulses,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1748–1752 (2009).
[CrossRef]

H. Pan, E. Wu, H. Dong, and H. Zeng, “Single-photon frequency up-conversion with multimode pumping,” Phys. Rev. A 77(3), 033815 (2008).
[CrossRef]

Wu, G.

Yamamoto, Y.

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fiber,” New J. Phys. 7, 232 (2005).
[CrossRef]

Yaman, F.

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75(2), 023803 (2007).
[CrossRef]

Zbinden, H.

E. Pomarico, B. Sanguinetti, R. Thew, and H. Zbinden, “Room temperature photon number resolving detector for infared wavelengths,” Opt. Express 18(10), 10750–10759 (2010).
[CrossRef] [PubMed]

R. T. Thew, H. Zbinden, and N. Gisin, “Tunable upconversion photon detector,” Appl. Phys. Lett. 93(7), 071104 (2008).
[CrossRef]

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437(7055), 116–120 (2005).
[CrossRef] [PubMed]

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
[CrossRef]

Zeilinger, A.

D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Zeng, H.

K. Huang, X. Gu, M. Ren, Y. Jian, H. Pan, G. Wu, E. Wu, and H. Zeng, “Photon-number-resolving detection at 1.04 μm via coincidence frequency upconversion,” Opt. Lett. 36(9), 1722–1724 (2011).
[CrossRef] [PubMed]

X. Gu, K. Huang, Y. Li, H. Pan, E. Wu, and H. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010).
[CrossRef]

X. Gu, Y. Li, H. Pan, E. Wu, and H. Zeng, “High-speed single-photon frequency upconversion with synchronous pump pulses,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1748–1752 (2009).
[CrossRef]

H. Pan, E. Wu, H. Dong, and H. Zeng, “Single-photon frequency up-conversion with multimode pumping,” Phys. Rev. A 77(3), 033815 (2008).
[CrossRef]

H. Pan and H. Zeng, “Efficient and stable single-photon counting at 1.55 microm by intracavity frequency upconversion,” Opt. Lett. 31(6), 793–795 (2006).
[CrossRef] [PubMed]

Appl. Phys. B (1)

K. P. Petrov, S. Waltman, E. J. Dlugokencky, M. Arbore, M. M. Fejer, F. K. Tittel, and L. W. Hollberg, “Precise measurement of methane in air using diode-pumped 3.4-μm difference-frequency generation in PPLN,” Appl. Phys. B 64, 567–572 (1997).
[CrossRef]

Appl. Phys. Lett. (2)

R. T. Thew, H. Zbinden, and N. Gisin, “Tunable upconversion photon detector,” Appl. Phys. Lett. 93(7), 071104 (2008).
[CrossRef]

X. Gu, K. Huang, Y. Li, H. Pan, E. Wu, and H. Zeng, “Temporal and spectral control of single-photon frequency upconversion for pulsed radiation,” Appl. Phys. Lett. 96(13), 131111 (2010).
[CrossRef]

Eur. Phys. J. D (2)

A. Beveratos, S. Kühn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18(2), 191–196 (2002).
[CrossRef]

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18(2), 155–160 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

X. Gu, Y. Li, H. Pan, E. Wu, and H. Zeng, “High-speed single-photon frequency upconversion with synchronous pump pulses,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1748–1752 (2009).
[CrossRef]

Nat. Photonics (1)

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

Nature (2)

D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[CrossRef]

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437(7055), 116–120 (2005).
[CrossRef] [PubMed]

New J. Phys. (4)

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-IIPPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010).
[CrossRef]

J. Chen, F. K. Lee, X. Li, L. P. Voss, and P. Kumar, “Schemes for fiber-based entanglement generation in the telecom band,” New J. Phys. 9(8), 289 (2007).
[CrossRef]

J. Chen, J. B. Altepeter, and P. Kumar, “Quantum-state engineering using nonlinear optical Sangac loops,” New J. Phys. 10(12), 123019 (2008).
[CrossRef]

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fiber,” New J. Phys. 7, 232 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. A (4)

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81(2), 021801 (2010).
[CrossRef]

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70(3), 031802 (2004).
[CrossRef]

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75(2), 023803 (2007).
[CrossRef]

H. Pan, E. Wu, H. Dong, and H. Zeng, “Single-photon frequency up-conversion with multimode pumping,” Phys. Rev. A 77(3), 033815 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

H. Takesue, “Erasing distinguishability using quantum frequency up-conversion,” Phys. Rev. Lett. 101(17), 173901 (2008).
[CrossRef] [PubMed]

J. M. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153–2156 (1992).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup of the correlation detection in single-photon frequency upconversion. DM, dichroic mirror with HR at 1.04 µm and AR at 1.55 µm; GP, Glan prism; PPLN, periodically poled lithium niobate crystal; HWP, half-wave plate; D1, D2, Si-APD single-photon detectors.

Fig. 2
Fig. 2

SFG signal and the unconverted infrared signal intensity as a function of the pump power.

Fig. 3
Fig. 3

Coincidence measurement between the SFG photons and the unconverted infrared photons dependent on the conversion efficiency.

Fig. 4
Fig. 4

Intensity cross-correlation of the SFG photons and unconverted infrared photons at different conversion efficiencies.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

H ^ =iχ E p ( a ^ 1 a ^ 2 +H.c.),
|ϕ=| ψ 1 , 0 2 ,
a ^ 1 (L)= a ^ 1 (0)cos(|g E p |L) a ^ 2 (0)sin(|g E p |L),
a ^ 2 (L)= a ^ 2 (0)cos(|g E p |L)+ a ^ 1 (0)sin(|g E p |L),
n ^ 1 = a ^ 1 (L) a ^ 1 (L) = ϕ| [ a ^ 1 (0)cos(|g E p |L) a ^ 2 (0)sin(|g E p |L)] [ a ^ 1 (0)cos(|g E p |L) a ^ 2 (0)sin(|g E p |L)]|ϕ,
0 2 | a ^ 2 (0)= a ^ 2 (0)| 0 2 =0.
n ^ 1 = ψ 1 | a ^ 1 (0) a ^ 1 (0)| ψ 1 cos 2 (|g E p |L) = ψ 1 | n ^ 0 | ψ 1 cos 2 (|g E p |L),
n ^ 2 = a ^ 2 (L) a ^ 2 (L) = ψ 1 | n ^ 0 | ψ 1 sin 2 (|g E p |L),
n ^ 1 n ^ 2 = a ^ 1 (L) a ^ 2 (L) a ^ 2 (L) a ^ 1 (L) =[ n ^ 2 0 n ^ 0 ] cos 2 (|g E p |L) sin 2 (|g E p |L),
η= sin 2 (|g E p |L),
n ^ 1 n ^ 2 =[ n ^ 2 0 n ^ 0 ]η(1η),
g (2) (0)= n ^ 1 n ^ 2 n ^ 1 n ^ 2 = n ^ 2 0 n ^ 0 n ^ 0 2 ,
H ^ =i ij χ E pi ( a ^ 1j a ^ 2ij H.c.),
d a ^ 1j dt = 1 ih [ a ^ 1j , a ^ 1j a ^ 2 H ^ ]=g i E pi a ^ 2ij d a ^ 2ij dt = 1 ih [ a ^ 2ij , H ^ ]=g E pi a ^ 1j .
a ^ 1 = i a ^ 1j a ^ 2 = j i C i a ^ 2ij ,( i C i 2 =1),
a ^ 1 (L)= a ^ 1 (0)cos(|g E p |L) a ^ 2 (0)sin(|g E p |L),
a ^ 2 (L)= a ^ 2 (0)cos(|g E p |L)+ a ^ 1 (0)sin(|g E p |L).
g (2) (0)= N C N 1 N 2 R T acq .

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