Abstract

We report a simple scheme for direct generation of frequency-bin entangled photon pairs via spontaneous parametric downconversion. Our fabricated nonlinear optical crystal with two different poling periods can simultaneously satisfy two different, spectrally symmetric nondegenerate quasi-phase-matching conditions, enabling the direct generation of entanglement in two discrete frequency-bin modes. Our produced photon pairs exhibited Hong-Ou-Mandel interference with high-visibility beating oscillations— a signature of two-mode frequency-bin entanglement. Moreover, we demonstrate deterministic entanglement-mode conversion from frequency-bin to polarization modes, with which our source can be more versatile for various quantum applications. Our scheme can be extended to direct generation of high-dimensional frequency-bin entanglement, and thus will be a key technology for frequency-multiplexed optical quantum information processing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]
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    [Crossref]
  3. J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, and A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Reviews of Modern Physics 84, 777–838 (2012).
    [Crossref]
  4. C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Physical Review Letters 59, 2044–2046 (1987).
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  5. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
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  6. W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Physical Review A 64, 063815 (2001).
    [Crossref]
  7. A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Physical Review Letters 99, 243601 (2007).
    [Crossref]
  8. P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, “Conditional preparation of single photons using parametric downconversion: a recipe for purity,” New Journal of Physics 10, 093011 (2008).
    [Crossref]
  9. P. G. Evans, R. S. Bennink, W. P. Grice, T. S. Humble, and J. Schaake, “Bright source of spectrally uncorrelated polarization-entangled photons with nearly single-mode emission,” Physical Review Letters 105, 253601 (2010).
    [Crossref]
  10. M. Yabuno, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Four-photon quantum interferometry at a telecom wavelength,” Physical Review A 86, 010302 (2012).
    [Crossref]
  11. F. Kaneda, K. Garay-Palmett, A. B. U’Ren, and P. G. Kwiat, “Heralded single-photon source utilizing highly nondegenerate, spectrally factorable spontaneous parametric downconversion,” Optics Express 24, 10733–10747 (2016).
    [Crossref] [PubMed]
  12. C. Chen, C. Bo, M. Y. Niu, F. Xu, Z. Zhang, J. H. Shapiro, and F. N. C. Wong, “Efficient generation and characterization of spectrally factorable biphotons,” Optics Express 25, 7300–7312 (2017).
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  15. M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New Journal of Physics 17, 033033 (2015).
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  16. K. McCusker and P. G. Kwiat, “Efficient Optical Quantum State Engineering,” Physical Review Letters 103, 163602 (2009).
    [Crossref] [PubMed]
  17. F. Kaneda, B. G. Christensen, J. J. Wong, H. S. Park, K. T. McCusker, and P. G. Kwiat, “Time-Multiplexed Heralded Single-Photon Source,” Optica 2, 1010–1013 (2015).
    [Crossref]
  18. F. Kaneda, F. Xu, J. Chapman, and P. G. Kwiat, “Quantum-memory-assisted multi-photon generation for efficient quantum information processing,” Optica 4, 1034–1037 (2017).
    [Crossref]
  19. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature 412, 417–419 (2001).
    [Crossref] [PubMed]
  20. M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Physical Review Letters 100, 183601 (2008).
    [Crossref] [PubMed]
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    [Crossref]
  22. M. Nakatani, R. Shimizu, and K. Koshino, “Up-conversion dynamics for temporally entangled two-photon pulses,” Physical Review A 83, 013824 (2011).
    [Crossref]
  23. Z. Ou and L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Physical Review Letters 61, 54–57 (1988).
    [Crossref] [PubMed]
  24. J. Rarity and P. Tapster, “Two-color photons and nonlocality in fourth-order interference,” Physical Review A 41, 5139 (1990).
    [Crossref]
  25. Y. Shih and A. Sergienko, “Observation of quantum beating in a simple beam-splitting experiment: Two-particle entanglement in spin and space-time,” Physical Review A 50, 2564–2568 (1994).
    [Crossref]
  26. X. Li, L. Yang, X. Ma, L. Cui, Z. Y. Ou, and D. Yu, “All-fiber source of frequency-entangled photon pairs,” Physical Review A 79, 033817 (2009).
    [Crossref]
  27. Q. Zhou, W. Zhang, C. Yuan, Y. Huang, and J. Peng, “Generation of 1.5 μm discrete frequency-entangled two-photon state in polarization-maintaining fibers,” Optics letters 39, 2109–2112 (2014).
    [Crossref]
  28. Q. Zhou, S. Dong, W. Zhang, L. You, Y. He, W. Zhang, Y. Huang, and J. Peng, “Frequency-entanglement preparation based on the coherent manipulation of frequency nondegenerate energy-time entangled state,” Journal of the Optical Society of America B-Optical Physics 31, 1801–1806 (2014).
    [Crossref]
  29. S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete Tunable Color Entanglement,” Physical Review Letters 103, 253601 (2009).
    [Crossref]
  30. R.-B. Jin, R. Shimizu, M. Fujiwara, M. Takeoka, R. Wakabayashi, T. Yamashita, S. Miki, H. Terai, T. Gerrits, and M. Sasaki, “Simple method of generating and distributing frequency-entangled qudits,” Quantum Science and Technology 1, 015004 (2016).
    [Crossref]
  31. R.-B. Jin, R. Shiina, and R. Shimizu, “Quantum manipulation of biphoton spectral distributions in a 2D frequency space toward arbitrary shaping of a biphoton wave packet,” Optics Express 26, 21153–21158 (2018).
    [Crossref]
  32. H. Kim, H. J. Lee, S. M. Lee, and H. S. Moon, “Highly efficient source for frequency-entangled photon pairs generated in a 3rd-order periodically poled MgO-doped stoichiometric LiTaO3 crystal,” Optics letters 40, 3061–3064 (2015).
    [Crossref]
  33. Z. Xie, T. Zhong, S. Shrestha, X. A. Xu, J. Liang, Y. X. Gong, J. C. Bienfang, A. Restelli, J. H. Shapiro, F. N. C. Wong, and C. W. Wong, “Harnessing high-dimensional hyperentanglement through a biphoton frequency comb,” Nature Photonics 9, 536–543 (2015).
    [Crossref]
  34. W. Ueno, F. Kaneda, H. Suzuki, S. Nagano, A. Syouji, R. Shimizu, K. Suizu, and K. Edamatsu, “Entangled photon generation in two-period quasi-phase-matched parametric down-conversion,” Optics Express 20, 5508–5517 (2012).
    [Crossref]
  35. H. Herrmann, X. Yang, A. Thomas, A. Poppe, W. Sohler, and C. Silberhorn, “Post-selection free, integrated optical source of non-degenerate, polarization entangled photon pairs,” Optics Express 21, 27981 (2013).
    [Crossref]
  36. M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Physics Letters 22, 243–244 (1966).
    [Crossref]
  37. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Optics letters 22, 1553–1555 (1997).
    [Crossref]
  38. T.-M. Zhao, H. Zhang, J. Yang, Z.-R. Sang, X. Jiang, X.-H. Bao, and J.-W. Pan, “Entangling Different-Color Photons via Time-Resolved Measurement and Active Feed Forward,” Physical Review Letters 112, 103602 (2014).
    [Crossref]
  39. M. Rubin, D. Klyshko, Y. Shih, and A. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Physical Review A 50, 5122–5133 (1994).
    [Crossref]
  40. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Physical Review A 64, 052312 (2001).
    [Crossref]
  41. K. Wang, “Quantum theory of two-photon wavepacket interference in a beamsplitter,” Journal of Physics B: Atomic, Molecular and Optical Physics 39, R293–R324 (2006).
    [Crossref]
  42. A. Fedrizzi, T. Herbst, M. Aspelmeyer, M. Barbieri, T. Jennewein, and A. Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New Journal of Physics 11, 103052 (2009).
    [Crossref]

2018 (1)

R.-B. Jin, R. Shiina, and R. Shimizu, “Quantum manipulation of biphoton spectral distributions in a 2D frequency space toward arbitrary shaping of a biphoton wave packet,” Optics Express 26, 21153–21158 (2018).
[Crossref]

2017 (2)

C. Chen, C. Bo, M. Y. Niu, F. Xu, Z. Zhang, J. H. Shapiro, and F. N. C. Wong, “Efficient generation and characterization of spectrally factorable biphotons,” Optics Express 25, 7300–7312 (2017).
[Crossref] [PubMed]

F. Kaneda, F. Xu, J. Chapman, and P. G. Kwiat, “Quantum-memory-assisted multi-photon generation for efficient quantum information processing,” Optica 4, 1034–1037 (2017).
[Crossref]

2016 (2)

R.-B. Jin, R. Shimizu, M. Fujiwara, M. Takeoka, R. Wakabayashi, T. Yamashita, S. Miki, H. Terai, T. Gerrits, and M. Sasaki, “Simple method of generating and distributing frequency-entangled qudits,” Quantum Science and Technology 1, 015004 (2016).
[Crossref]

F. Kaneda, K. Garay-Palmett, A. B. U’Ren, and P. G. Kwiat, “Heralded single-photon source utilizing highly nondegenerate, spectrally factorable spontaneous parametric downconversion,” Optics Express 24, 10733–10747 (2016).
[Crossref] [PubMed]

2015 (6)

M. Okano, H. H. Lim, R. Okamoto, N. Nishizawa, S. Kurimura, and S. Takeuchi, “m resolution two-photon interference with dispersion cancellation for quantum optical coherence tomography,” Scientific Reports 5, 18042 (2015).
[Crossref]

H. Kim, H. J. Lee, S. M. Lee, and H. S. Moon, “Highly efficient source for frequency-entangled photon pairs generated in a 3rd-order periodically poled MgO-doped stoichiometric LiTaO3 crystal,” Optics letters 40, 3061–3064 (2015).
[Crossref]

Z. Xie, T. Zhong, S. Shrestha, X. A. Xu, J. Liang, Y. X. Gong, J. C. Bienfang, A. Restelli, J. H. Shapiro, F. N. C. Wong, and C. W. Wong, “Harnessing high-dimensional hyperentanglement through a biphoton frequency comb,” Nature Photonics 9, 536–543 (2015).
[Crossref]

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding,” New Journal of Physics 17, 022002 (2015).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New Journal of Physics 17, 033033 (2015).
[Crossref]

F. Kaneda, B. G. Christensen, J. J. Wong, H. S. Park, K. T. McCusker, and P. G. Kwiat, “Time-Multiplexed Heralded Single-Photon Source,” Optica 2, 1010–1013 (2015).
[Crossref]

2014 (3)

T.-M. Zhao, H. Zhang, J. Yang, Z.-R. Sang, X. Jiang, X.-H. Bao, and J.-W. Pan, “Entangling Different-Color Photons via Time-Resolved Measurement and Active Feed Forward,” Physical Review Letters 112, 103602 (2014).
[Crossref]

Q. Zhou, W. Zhang, C. Yuan, Y. Huang, and J. Peng, “Generation of 1.5 μm discrete frequency-entangled two-photon state in polarization-maintaining fibers,” Optics letters 39, 2109–2112 (2014).
[Crossref]

Q. Zhou, S. Dong, W. Zhang, L. You, Y. He, W. Zhang, Y. Huang, and J. Peng, “Frequency-entanglement preparation based on the coherent manipulation of frequency nondegenerate energy-time entangled state,” Journal of the Optical Society of America B-Optical Physics 31, 1801–1806 (2014).
[Crossref]

2013 (1)

H. Herrmann, X. Yang, A. Thomas, A. Poppe, W. Sohler, and C. Silberhorn, “Post-selection free, integrated optical source of non-degenerate, polarization entangled photon pairs,” Optics Express 21, 27981 (2013).
[Crossref]

2012 (3)

W. Ueno, F. Kaneda, H. Suzuki, S. Nagano, A. Syouji, R. Shimizu, K. Suizu, and K. Edamatsu, “Entangled photon generation in two-period quasi-phase-matched parametric down-conversion,” Optics Express 20, 5508–5517 (2012).
[Crossref]

M. Yabuno, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Four-photon quantum interferometry at a telecom wavelength,” Physical Review A 86, 010302 (2012).
[Crossref]

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, and A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Reviews of Modern Physics 84, 777–838 (2012).
[Crossref]

2011 (1)

M. Nakatani, R. Shimizu, and K. Koshino, “Up-conversion dynamics for temporally entangled two-photon pulses,” Physical Review A 83, 013824 (2011).
[Crossref]

2010 (2)

P. G. Evans, R. S. Bennink, W. P. Grice, T. S. Humble, and J. Schaake, “Bright source of spectrally uncorrelated polarization-entangled photons with nearly single-mode emission,” Physical Review Letters 105, 253601 (2010).
[Crossref]

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. M. Merolla, and K. Huy, “Frequency-bin entangled photons,” Physical Review A 82, 013804 (2010).
[Crossref]

2009 (4)

K. McCusker and P. G. Kwiat, “Efficient Optical Quantum State Engineering,” Physical Review Letters 103, 163602 (2009).
[Crossref] [PubMed]

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete Tunable Color Entanglement,” Physical Review Letters 103, 253601 (2009).
[Crossref]

X. Li, L. Yang, X. Ma, L. Cui, Z. Y. Ou, and D. Yu, “All-fiber source of frequency-entangled photon pairs,” Physical Review A 79, 033817 (2009).
[Crossref]

A. Fedrizzi, T. Herbst, M. Aspelmeyer, M. Barbieri, T. Jennewein, and A. Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New Journal of Physics 11, 103052 (2009).
[Crossref]

2008 (2)

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Physical Review Letters 100, 183601 (2008).
[Crossref] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, “Conditional preparation of single photons using parametric downconversion: a recipe for purity,” New Journal of Physics 10, 093011 (2008).
[Crossref]

2007 (2)

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Physical Review Letters 99, 243601 (2007).
[Crossref]

K. Edamatsu, “Entangled Photons: Generation, Observation, and Characterization,” Japanese Journal of Applied Physics 46, 7175–7187 (2007).
[Crossref]

2006 (1)

K. Wang, “Quantum theory of two-photon wavepacket interference in a beamsplitter,” Journal of Physics B: Atomic, Molecular and Optical Physics 39, R293–R324 (2006).
[Crossref]

2001 (4)

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Physical Review A 64, 052312 (2001).
[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Physical Review A 64, 063815 (2001).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature 412, 417–419 (2001).
[Crossref] [PubMed]

1997 (1)

D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Optics letters 22, 1553–1555 (1997).
[Crossref]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Physical Review Letters 75, 4337–4341 (1995).
[Crossref] [PubMed]

1994 (2)

Y. Shih and A. Sergienko, “Observation of quantum beating in a simple beam-splitting experiment: Two-particle entanglement in spin and space-time,” Physical Review A 50, 2564–2568 (1994).
[Crossref]

M. Rubin, D. Klyshko, Y. Shih, and A. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Physical Review A 50, 5122–5133 (1994).
[Crossref]

1990 (1)

J. Rarity and P. Tapster, “Two-color photons and nonlocality in fourth-order interference,” Physical Review A 41, 5139 (1990).
[Crossref]

1988 (1)

Z. Ou and L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Physical Review Letters 61, 54–57 (1988).
[Crossref] [PubMed]

1987 (1)

C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Physical Review Letters 59, 2044–2046 (1987).
[Crossref] [PubMed]

1966 (1)

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Physics Letters 22, 243–244 (1966).
[Crossref]

Aspelmeyer, M.

A. Fedrizzi, T. Herbst, M. Aspelmeyer, M. Barbieri, T. Jennewein, and A. Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New Journal of Physics 11, 103052 (2009).
[Crossref]

Bao, X.-H.

T.-M. Zhao, H. Zhang, J. Yang, Z.-R. Sang, X. Jiang, X.-H. Bao, and J.-W. Pan, “Entangling Different-Color Photons via Time-Resolved Measurement and Active Feed Forward,” Physical Review Letters 112, 103602 (2014).
[Crossref]

Barbieri, M.

A. Fedrizzi, T. Herbst, M. Aspelmeyer, M. Barbieri, T. Jennewein, and A. Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New Journal of Physics 11, 103052 (2009).
[Crossref]

Bennink, R. S.

P. G. Evans, R. S. Bennink, W. P. Grice, T. S. Humble, and J. Schaake, “Bright source of spectrally uncorrelated polarization-entangled photons with nearly single-mode emission,” Physical Review Letters 105, 253601 (2010).
[Crossref]

Bienfang, J. C.

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding,” New Journal of Physics 17, 022002 (2015).
[Crossref]

Z. Xie, T. Zhong, S. Shrestha, X. A. Xu, J. Liang, Y. X. Gong, J. C. Bienfang, A. Restelli, J. H. Shapiro, F. N. C. Wong, and C. W. Wong, “Harnessing high-dimensional hyperentanglement through a biphoton frequency comb,” Nature Photonics 9, 536–543 (2015).
[Crossref]

Bo, C.

C. Chen, C. Bo, M. Y. Niu, F. Xu, Z. Zhang, J. H. Shapiro, and F. N. C. Wong, “Efficient generation and characterization of spectrally factorable biphotons,” Optics Express 25, 7300–7312 (2017).
[Crossref] [PubMed]

Boyd, R. W.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New Journal of Physics 17, 033033 (2015).
[Crossref]

Carrasco, S.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Physical Review Letters 100, 183601 (2008).
[Crossref] [PubMed]

Ceré, A.

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Physical Review Letters 99, 243601 (2007).
[Crossref]

Chapman, J.

Chen, C.

C. Chen, C. Bo, M. Y. Niu, F. Xu, Z. Zhang, J. H. Shapiro, and F. N. C. Wong, “Efficient generation and characterization of spectrally factorable biphotons,” Optics Express 25, 7300–7312 (2017).
[Crossref] [PubMed]

Chen, Z.-B.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, and A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Reviews of Modern Physics 84, 777–838 (2012).
[Crossref]

Christensen, B. G.

Cui, L.

X. Li, L. Yang, X. Ma, L. Cui, Z. Y. Ou, and D. Yu, “All-fiber source of frequency-entangled photon pairs,” Physical Review A 79, 033817 (2009).
[Crossref]

Cussey, J.

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. M. Merolla, and K. Huy, “Frequency-bin entangled photons,” Physical Review A 82, 013804 (2010).
[Crossref]

Dong, S.

Q. Zhou, S. Dong, W. Zhang, L. You, Y. He, W. Zhang, Y. Huang, and J. Peng, “Frequency-entanglement preparation based on the coherent manipulation of frequency nondegenerate energy-time entangled state,” Journal of the Optical Society of America B-Optical Physics 31, 1801–1806 (2014).
[Crossref]

Edamatsu, K.

M. Yabuno, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Four-photon quantum interferometry at a telecom wavelength,” Physical Review A 86, 010302 (2012).
[Crossref]

W. Ueno, F. Kaneda, H. Suzuki, S. Nagano, A. Syouji, R. Shimizu, K. Suizu, and K. Edamatsu, “Entangled photon generation in two-period quasi-phase-matched parametric down-conversion,” Optics Express 20, 5508–5517 (2012).
[Crossref]

K. Edamatsu, “Entangled Photons: Generation, Observation, and Characterization,” Japanese Journal of Applied Physics 46, 7175–7187 (2007).
[Crossref]

Emplit, P.

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. M. Merolla, and K. Huy, “Frequency-bin entangled photons,” Physical Review A 82, 013804 (2010).
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P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, “Conditional preparation of single photons using parametric downconversion: a recipe for purity,” New Journal of Physics 10, 093011 (2008).
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L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. M. Merolla, and K. Huy, “Frequency-bin entangled photons,” Physical Review A 82, 013804 (2010).
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L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. M. Merolla, and K. Huy, “Frequency-bin entangled photons,” Physical Review A 82, 013804 (2010).
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Z. Ou and L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Physical Review Letters 61, 54–57 (1988).
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X. Li, L. Yang, X. Ma, L. Cui, Z. Y. Ou, and D. Yu, “All-fiber source of frequency-entangled photon pairs,” Physical Review A 79, 033817 (2009).
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Zhang, Z.

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Figures (4)

Fig. 1
Fig. 1 Schematic diagram of the generation of frequency-bin entangled photon pairs. (a) The illustration of two-period QPM crystal. (b) Frequency-bin entanglement generation. (c) Polarization entanglement generation demonstrated in [34]. PBS: polarizing beamsplitter, DM: dichroic mirror. (d) Theoretical tuning curves for a PPLN crystal with our designed poling periods ( Λ 1 = 9.25 μm and Λ2 = 9.50 μm) and a pump wavelength of 775 nm.
Fig. 2
Fig. 2 Illustration of the experimental setup for (a) generation and detection of frequency-bin entangled photons and (b) detection of polarization entanglement. PPLN: periodically poled lithium niobate, PBS: polarizing beamsplitter, QWP: quarter-wave plate, HWP: half-wave plate, SMF: single-mode fiber, SPD: single-photon detector, DM: dichroic mirror, PA: polarization analyzer. Each PA consists of a QWP, a HWP, and a PBS.
Fig. 3
Fig. 3 Characterization of the frequency-bin entanglment. (a) Observed HOM interference for (a) -3 ps τ 3 ps and (b) -0.5 ps τ 0.5 ps. (c) Reconstructed density matrix. Error bars were calculated from Poissonian photon-counting statistics.
Fig. 4
Fig. 4 Measured polarization-mode density matrices after the entanglement-mode transfer for τ = (a) 0 fs, (b) 47 fs, and (c) -20 fs.

Tables (1)

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Table 1 Characteristics of the polarization-mode density matrices. τ, time delay in the Michelson interferometer; I ( τ ) / N, normalized coincidence count rate in the HOMI; ϕ, phase of the frequency entangled state predicted from the HOMI; F, state fidelity to the ideal density matrix | ψ p for ϕ; C, concurrence.

Equations (8)

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| FB n = j = 1 n 1 n | ω j | ω n j + 1 ,
Δ ω = ω p ω s ω i = 0 ,
Δ k = k p k s k i 2 π Λ 1 ( 2 ) = 0 ,
| ψ = 1 2 ( | H , ω 1 | V , ω 2 + e i ϕ | V , ω 1 | H , ω 2 ) ,
| ψ f = 1 2 ( | ω 1 A , H | ω 2 B , V + e i ϕ | ω 2 A , H | ω 1 B , V ) ,
| ψ p = 1 2 ( | H A , ω 1 | V B , ω 2 + e i ϕ | V A , ω 1 | H B , ω 2 ) .
I ( τ ) = { N 2 { 1 V cos  ( δ ω τ ) ( 1 | τ τ c | ) } for | τ | τ c N 2 for | τ | > τ c
ρ F = p | ω 1 ω 2 ω 1 ω 2 | A B + ( 1 p ) | ω 2 ω 1 ω 2 ω 1 | A B + V 2 ( e i ϕ | ω 1 ω 2 ω 2 ω 1 | A B + e i ϕ | ω 2 ω 1 ω 1 ω 2 | A B ) ,

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