Abstract

We demonstrate a method to generate entangled photons with controlled spatial shape by parametric down conversion (PDC) in a 2D nonlinear crystal. A compact and novel crystal source was designed and fabricated, generating directly path entangled photons without the use of additional beam-splitters. This crystal supports two PDC processes, emitting biphotons into two beamlike modes simultaneously. Two coherent path entangled amplitudes of biphotons were created and their interference observed. Our method enables the generation of entangled photons with controlled spatial, spectral and polarization properties.

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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, 4337–4341 (1995).
    [CrossRef] [PubMed]
  2. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  3. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [CrossRef]
  4. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
    [CrossRef]
  5. N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
    [CrossRef]
  6. J. P. Torres, A. Alexandrescu, S. Carrasco, and L. Torner, “Quasi-phase-matching engineering for spatial control of entangled two-photon states,” Opt. Lett. 29, 376–378 (2004).
    [CrossRef] [PubMed]
  7. H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
    [CrossRef] [PubMed]
  8. R. Shiloh and A. Arie, “Spectral and temporal holograms with nonlinear optics,” Opt. Lett. 37, 3591–3593 (2012).
    [CrossRef] [PubMed]
  9. R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
    [CrossRef] [PubMed]
  10. S. N. Zhu, Y. Y Zhu, and N. B Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
    [CrossRef]
  11. V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
    [CrossRef]
  12. N. Broderick, G. Ross, H. Offerhaus, D. Richardson, and D. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
    [CrossRef] [PubMed]
  13. J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
    [CrossRef] [PubMed]
  14. J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, and M. C. Teich, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).
    [CrossRef] [PubMed]
  15. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
    [CrossRef] [PubMed]
  16. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature (London) 429, 161–164 (2004).
    [CrossRef]
  17. T. Nagata, R. Okamoto, J. L. OBrien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
    [CrossRef] [PubMed]
  18. I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
    [CrossRef] [PubMed]
  19. C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
    [CrossRef]
  20. T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
    [CrossRef]
  21. Y.-H. Kim, “Quantum interference with beamlike type-II spontaneous parametric down-conversion,” Phys. Rev. A 68, 013804 (2003).
    [CrossRef]
  22. A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quant. Electron. 39, 361–375 (2007).
    [CrossRef]
  23. Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ?(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
    [CrossRef]
  24. J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie Waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
    [CrossRef] [PubMed]
  25. I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96, 423–432 (2009).
    [CrossRef]
  26. M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1992).
    [CrossRef]
  27. D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (2009).
    [CrossRef]
  28. K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
    [CrossRef] [PubMed]
  29. M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
    [CrossRef] [PubMed]
  30. Y.-X. Gong, P. Xu, J. Shi, L. Chen, X. Q. Yu, P. Xue, and S. N. Zhu, “Generation of polarization-entangled photon pairs via concurrent spontaneous parametric downconversions in a single ?(2) nonlinear photonic crystal,” Opt. Lett. 37, 4374–4376 (2012).
    [CrossRef] [PubMed]
  31. H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, and S. N. Zhu, “Compact engineering of path entangled sources from a monolithic quadratic nonlinear photonic crystal,” http://arxiv.org/abs/1302.0162.

2012

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

R. Shiloh and A. Arie, “Spectral and temporal holograms with nonlinear optics,” Opt. Lett. 37, 3591–3593 (2012).
[CrossRef] [PubMed]

Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ?(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
[CrossRef]

Y.-X. Gong, P. Xu, J. Shi, L. Chen, X. Q. Yu, P. Xue, and S. N. Zhu, “Generation of polarization-entangled photon pairs via concurrent spontaneous parametric downconversions in a single ?(2) nonlinear photonic crystal,” Opt. Lett. 37, 4374–4376 (2012).
[CrossRef] [PubMed]

2011

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef] [PubMed]

2010

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[CrossRef] [PubMed]

2009

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96, 423–432 (2009).
[CrossRef]

D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

2007

T. Nagata, R. Okamoto, J. L. OBrien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[CrossRef] [PubMed]

A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quant. Electron. 39, 361–375 (2007).
[CrossRef]

2006

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[CrossRef]

2005

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

2004

J. P. Torres, A. Alexandrescu, S. Carrasco, and L. Torner, “Quasi-phase-matching engineering for spatial control of entangled two-photon states,” Opt. Lett. 29, 376–378 (2004).
[CrossRef] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature (London) 429, 161–164 (2004).
[CrossRef]

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[CrossRef]

2003

Y.-H. Kim, “Quantum interference with beamlike type-II spontaneous parametric down-conversion,” Phys. Rev. A 68, 013804 (2003).
[CrossRef]

2002

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

2000

N. Broderick, G. Ross, H. Offerhaus, D. Richardson, and D. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

1998

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

1997

S. N. Zhu, Y. Y Zhu, and N. B Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

1996

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[CrossRef] [PubMed]

1995

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, 4337–4341 (1995).
[CrossRef] [PubMed]

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie Waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef] [PubMed]

1993

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[CrossRef] [PubMed]

1992

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1992).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

1990

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, and M. C. Teich, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).
[CrossRef] [PubMed]

1987

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Afek, I.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[CrossRef] [PubMed]

Alexandrescu, A.

Ambar, O.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[CrossRef] [PubMed]

Arie, A.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

R. Shiloh and A. Arie, “Spectral and temporal holograms with nonlinear optics,” Opt. Lett. 37, 3591–3593 (2012).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96, 423–432 (2009).
[CrossRef]

A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quant. Electron. 39, 361–375 (2007).
[CrossRef]

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Bahabad, A.

A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quant. Electron. 39, 361–375 (2007).
[CrossRef]

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

Bai, Y. F.

Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ?(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
[CrossRef]

Beck, M.

D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (2009).
[CrossRef]

Berger, V.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

Bhandari, S.

D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (2009).
[CrossRef]

Björk, G.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie Waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef] [PubMed]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Bollinger, J. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[CrossRef] [PubMed]

Branning, D.

D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (2009).
[CrossRef]

Broderick, N.

N. Broderick, G. Ross, H. Offerhaus, D. Richardson, and D. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

Burnett, K.

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[CrossRef] [PubMed]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Campos, R. A.

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, and M. C. Teich, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).
[CrossRef] [PubMed]

Carrasco, S.

Chen, L.

Chuang, I.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie Waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef] [PubMed]

Dolev, I.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96, 423–432 (2009).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Edamatsu, K.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Fiorentino, M.

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[CrossRef]

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[CrossRef]

Gadret, G.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96, 423–432 (2009).
[CrossRef]

Ganany-Padowicz, A.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96, 423–432 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Gayer, O.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96, 423–432 (2009).
[CrossRef]

Gong, Y. X.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef] [PubMed]

H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, and S. N. Zhu, “Compact engineering of path entangled sources from a monolithic quadratic nonlinear photonic crystal,” http://arxiv.org/abs/1302.0162.

Gong, Y.-X.

Y.-X. Gong, P. Xu, J. Shi, L. Chen, X. Q. Yu, P. Xue, and S. N. Zhu, “Generation of polarization-entangled photon pairs via concurrent spontaneous parametric downconversions in a single ?(2) nonlinear photonic crystal,” Opt. Lett. 37, 4374–4376 (2012).
[CrossRef] [PubMed]

Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ?(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
[CrossRef]

Habshoosh, N.

A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quant. Electron. 39, 361–375 (2007).
[CrossRef]

Hanna, D.

N. Broderick, G. Ross, H. Offerhaus, D. Richardson, and D. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

Heinzen, D. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[CrossRef] [PubMed]

Holland, M. J.

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[CrossRef] [PubMed]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Itano, W. M.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[CrossRef] [PubMed]

Itoh, T.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Jacobson, J.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie Waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef] [PubMed]

Jakeman, E.

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, and M. C. Teich, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).
[CrossRef] [PubMed]

Jin, H.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef] [PubMed]

H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, and S. N. Zhu, “Compact engineering of path entangled sources from a monolithic quadratic nonlinear photonic crystal,” http://arxiv.org/abs/1302.0162.

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Juwiler, I.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

Kim, T.

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[CrossRef]

Kim, Y.-H.

Y.-H. Kim, “Quantum interference with beamlike type-II spontaneous parametric down-conversion,” Phys. Rev. A 68, 013804 (2003).
[CrossRef]

Kuklewicz, C. E.

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[CrossRef]

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, 4337–4341 (1995).
[CrossRef] [PubMed]

Larchuk, T.

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, and M. C. Teich, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).
[CrossRef] [PubMed]

Leng, H. Y.

Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ?(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
[CrossRef]

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef] [PubMed]

H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, and S. N. Zhu, “Compact engineering of path entangled sources from a monolithic quadratic nonlinear photonic crystal,” http://arxiv.org/abs/1302.0162.

Lifshitz, R.

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

Lundeen, J. S.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature (London) 429, 161–164 (2004).
[CrossRef]

Luo, X. W.

H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, and S. N. Zhu, “Compact engineering of path entangled sources from a monolithic quadratic nonlinear photonic crystal,” http://arxiv.org/abs/1302.0162.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Mangin, J.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96, 423–432 (2009).
[CrossRef]

Mattle, K.

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, 4337–4341 (1995).
[CrossRef] [PubMed]

Messin, G.

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[CrossRef]

Ming, N. B

S. N. Zhu, Y. Y Zhu, and N. B Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

Mitchell, M. W.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature (London) 429, 161–164 (2004).
[CrossRef]

Nada, N.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1992).
[CrossRef]

Nagata, T.

T. Nagata, R. Okamoto, J. L. OBrien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[CrossRef] [PubMed]

OBrien, J. L.

T. Nagata, R. Okamoto, J. L. OBrien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[CrossRef] [PubMed]

Offerhaus, H.

N. Broderick, G. Ross, H. Offerhaus, D. Richardson, and D. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

Okamoto, R.

T. Nagata, R. Okamoto, J. L. OBrien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[CrossRef] [PubMed]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Rarity, J. G.

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, and M. C. Teich, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).
[CrossRef] [PubMed]

Richardson, D.

N. Broderick, G. Ross, H. Offerhaus, D. Richardson, and D. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

Ross, G.

N. Broderick, G. Ross, H. Offerhaus, D. Richardson, and D. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

Saitoh, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1992).
[CrossRef]

Sasaki, K.

T. Nagata, R. Okamoto, J. L. OBrien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[CrossRef] [PubMed]

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, 4337–4341 (1995).
[CrossRef] [PubMed]

Shapira, A.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

Shapiro, J. H.

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[CrossRef]

Shemer, K.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

Shi, J.

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, 4337–4341 (1995).
[CrossRef] [PubMed]

Shiloh, R.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

R. Shiloh and A. Arie, “Spectral and temporal holograms with nonlinear optics,” Opt. Lett. 37, 3591–3593 (2012).
[CrossRef] [PubMed]

Shimizu, R.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Silberberg, Y.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[CrossRef] [PubMed]

Steinberg, A. M.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature (London) 429, 161–164 (2004).
[CrossRef]

Takeuchi, S.

T. Nagata, R. Okamoto, J. L. OBrien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[CrossRef] [PubMed]

Tapster, P. R.

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, and M. C. Teich, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).
[CrossRef] [PubMed]

Teich, M. C.

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, and M. C. Teich, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).
[CrossRef] [PubMed]

Torner, L.

Torres, J. P.

Voloch-Bloch, N.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Watanabe, K.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1992).
[CrossRef]

Weinfurter, H.

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, 4337–4341 (1995).
[CrossRef] [PubMed]

Wineland, D. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[CrossRef] [PubMed]

Wong, F. N. C.

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[CrossRef]

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[CrossRef]

Xie, Z. D.

Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ?(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
[CrossRef]

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef] [PubMed]

Xu, P.

Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ?(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
[CrossRef]

Y.-X. Gong, P. Xu, J. Shi, L. Chen, X. Q. Yu, P. Xue, and S. N. Zhu, “Generation of polarization-entangled photon pairs via concurrent spontaneous parametric downconversions in a single ?(2) nonlinear photonic crystal,” Opt. Lett. 37, 4374–4376 (2012).
[CrossRef] [PubMed]

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef] [PubMed]

H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, and S. N. Zhu, “Compact engineering of path entangled sources from a monolithic quadratic nonlinear photonic crystal,” http://arxiv.org/abs/1302.0162.

Xue, P.

Yamada, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1992).
[CrossRef]

Yamamoto, Y.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie Waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef] [PubMed]

Yang, J.

Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ?(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
[CrossRef]

Yu, X. Q.

Zeilinger, A.

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, 4337–4341 (1995).
[CrossRef] [PubMed]

Zhang, C.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef] [PubMed]

Zhu, S. N.

Y.-X. Gong, P. Xu, J. Shi, L. Chen, X. Q. Yu, P. Xue, and S. N. Zhu, “Generation of polarization-entangled photon pairs via concurrent spontaneous parametric downconversions in a single ?(2) nonlinear photonic crystal,” Opt. Lett. 37, 4374–4376 (2012).
[CrossRef] [PubMed]

Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ?(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
[CrossRef]

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef] [PubMed]

S. N. Zhu, Y. Y Zhu, and N. B Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, and S. N. Zhu, “Compact engineering of path entangled sources from a monolithic quadratic nonlinear photonic crystal,” http://arxiv.org/abs/1302.0162.

Zhu, Y. Y

S. N. Zhu, Y. Y Zhu, and N. B Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

Am. J. Phys.

D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (2009).
[CrossRef]

Appl. Phys. B

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96, 423–432 (2009).
[CrossRef]

Appl. Phys. Lett.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1992).
[CrossRef]

http://arxiv.org/abs/1302.0162.

H. Jin, P. Xu, X. W. Luo, H. Y. Leng, Y. X. Gong, and S. N. Zhu, “Compact engineering of path entangled sources from a monolithic quadratic nonlinear photonic crystal,” http://arxiv.org/abs/1302.0162.

IEEE J. Quantum Electron.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Nat. Commun.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef] [PubMed]

Nat. Photonics

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Nature (London)

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature (London) 429, 161–164 (2004).
[CrossRef]

Opt. Lett.

Opt. Quant. Electron.

A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quant. Electron. 39, 361–375 (2007).
[CrossRef]

Phys. Rev.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Phys. Rev. A

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[CrossRef]

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[CrossRef]

Y.-H. Kim, “Quantum interference with beamlike type-II spontaneous parametric down-conversion,” Phys. Rev. A 68, 013804 (2003).
[CrossRef]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[CrossRef] [PubMed]

Y.-X. Gong, P. Xu, Y. F. Bai, J. Yang, H. Y. Leng, Z. D. Xie, and S. N. Zhu, “Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ?(2) nonlinear photonic crystal,” Phys. Rev. A 86, 023835 (2012).
[CrossRef]

Phys. Rev. Lett.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie Waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[CrossRef] [PubMed]

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[CrossRef] [PubMed]

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, and M. C. Teich, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

N. Broderick, G. Ross, H. Offerhaus, D. Richardson, and D. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[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, 4337–4341 (1995).
[CrossRef] [PubMed]

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

Science

S. N. Zhu, Y. Y Zhu, and N. B Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

T. Nagata, R. Okamoto, J. L. OBrien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[CrossRef] [PubMed]

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) A reciprocal lattice representation of the momenta involved in the down-conversion processes in the crystal. (b) An alternative possible design that avoids the G2,0 circle. (c) The experimental setup (see main text for details).

Fig. 2
Fig. 2

A picture of the down-converted photons through a 3 nm bandpass filter centered at 808 nm. It was taken using a cooled sensitive camera placed after the pump filter [see Fig. 1(c)]. Inset: an optical microscope picture of the NPC.

Fig. 3
Fig. 3

(a) Single counts of the left (red circles) or right (black squares) port of the BS. No dependence on the relative delay between the two paths is observed. (b) Coincidence counts as a function of the relative delay between the two paths. Interference pattern in the coincidence counts is observed with a contrast of 72 ± 1%. The interference period is half of the photons’ wavelength. Error bars are calculated assuming Poissonian noise statistics.

Fig. 4
Fig. 4

The interference visibility as a function of the relative polarization rotation between the two paths. At zero angle the two paths are indistinguishable at the BFC and the visibility is maximal. When the polarization of only one path is rotated, distinguishability is introduced and the interference contrast decreases.

Equations (5)

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

k ¯ 2 w k ¯ w 1 k ¯ w 2 = G ¯ n ,
| ψ φ = 1 2 ( | 2 , 0 + e 2 i φ | 0 , 2 ) ,
m G x = | k ¯ 2 w | ( | k ¯ w 1 | + | k ¯ w 1 | ) cos ( θ ) , n G y = ( | k ¯ w 1 | + | k ¯ w 1 | ) sin ( θ ) .
G m , n x = 2 R ( n Λ x ) 2 + ( m Λ y ) 2 J 1 [ 2 π R ( m Λ x ) 2 + ( n Λ y ) 2 ] .
| ψ = 1 2 ( 1 e 2 i φ ) | ψ π 2 + 1 2 ( 1 + e 2 i φ ) | 1 , 1 .

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