Abstract

We report a bright source of polarization-entangled photon pairs using spontaneous parametric down-conversion (SPDC) in a 10 mm long type-II PPKTP crystal pumped by a broadband multi-mode diode laser with the coherence length of 330 μm. Ordinarily, the huge mismatch between the pump coherence length and the PPKTP length would degrade the polarization entanglement completely. By employing the universal Bell-state synthesizer scheme, we remove the spectral/temporal distinguishability of the biphoton amplitudes entirely to recover high-visibility and high-fidelity two-photon polarization entanglement. The pair detection rates are 7,000 pairs/mW via single-mode fibers (with 99.2% fidelity) and 90,900 pairs/mW via multi-mode fibers (with 96.8% fidelity). We also analyze the scheme theoretically to show the effect of broadband multi-mode pumping on the phase matching condition of the type-II PPKTP.

© 2016 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  39. O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser,” Opt. Express 17, 13059–13069 (2009).
    [Crossref] [PubMed]
  40. O. Kwon, K.-K. Park, Y.-S. Ra, Y.-S. Kim, and Y.-H. Kim, “Time-bin entangled photon pairs from spontaneous parametric down-conversion pumped by a cw multi-mode diode laser,” Opt. Express 21, 25492–25500 (2013).
    [Crossref] [PubMed]
  41. A. V. Sergienko, Y. Shih, and M. H. Rubin, “Experimental evaluation of a two-photon wave packet in type-II parametric downconversion,” J. Opt. Soc. Am. B 12, 859 (1996).
    [Crossref]
  42. Y.-H. Kim, “Measurement of one-photon and two-photon wave packets in spontaneous parametric downconversion,” J. Opt. Soc. Am. B 20, 1959 (2003).
    [Crossref]
  43. O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0⟩ + | 0,N⟩ state,” Phys. Rev. A 81, 063801 (2010).
    [Crossref]

2014 (2)

K. Liao, H. Yan, J. He, S. Du, Z.-M. Zhang, and S.-L. Zhu, “Subnatural-linewidth polarization-entangled photon pairs with controllable temporal with controllable temporal length,” Phys. Rev. Lett. 112, 243602 (2014).
[Crossref]

M. Muller, S. Bounouar, K.D. Jons, M. Glassl, and P. Michler, “On-demand generation of indistinguishable polarization-entangled photon pairs,” Nat. Photon. 8, 224 (2014).
[Crossref]

2013 (3)

2012 (4)

A. Predojevic, S. Grabher, and G. Weihs, “Pulsed Sagnac source of polarization entangled photon pairs,” Opt. Express 20, 25022–25029 (2012).
[Crossref] [PubMed]

T.Sh. Iskhakov, I.N. Agafonov, M.V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 105 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

F. Kaiser, A. Issautier, L.A. Ngah, O. Danila, H. Herrmann, W. Sohler, A. Martin, and S. Tanzilli, “High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels,” New J. Phys. 14085015 (2012).
[Crossref]

F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M.W. Mitchell, J.P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express 20, 9640–9649 (2012).
[Crossref] [PubMed]

2011 (1)

H.-P. Lo, A. Yabushita, C.-W. Luo, P. Chen, and T. Kobayashi, “Beamlike photon-pair generation for two-photon interference and polarization entanglement,” Phys. Rev. A 83, 022313 (2011).
[Crossref]

2010 (3)

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photon. 4, 553–556 (2010).
[Crossref]

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

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0⟩ + | 0,N⟩ state,” Phys. Rev. A 81, 063801 (2010).
[Crossref]

2009 (3)

2008 (4)

P. Trojek and H. Weinfurter, “Collinear source of polarization-entangled photon pairs at nondegenerate wavelengths,” Appl. Phys. Lett. 92, 211103 (2008).
[Crossref]

X.-L. Niu, Y.-F. Huang, G.-Y. Xiang, G.-C. Guo, and Z.Y. Ou, “Beamlike high-brightness source of polarization-entangled photon pairs,” Opt. Lett. 33, 968–970 (2008).
[Crossref] [PubMed]

M. Fiorentino and R.G. Beausoleil, “Compact sources of polarization-entangled photons,” Opt. Express 16, 20149–20156 (2008).
[Crossref] [PubMed]

O. Kuzucu and F.N.C. Wong, “Pulsed Sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77, 032314 (2008).
[Crossref]

2007 (2)

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-Resolution Mode-Spacing Measurement of the Blue-Violet Diode Laser Using Interference of Felds Created with Time Delays Greater than the Coherence Time,” Jpn. J. Appl. Phys. 46, 7720–7723 (2007).
[Crossref]

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15, 15377–15386 (2007).
[Crossref] [PubMed]

2006 (1)

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 (1)

2004 (2)

M. Pelton, P. Marsden, D. Ljunggren, M. Tengner, A. Karlsson, A. Fragemann, C. Canalias, and F. Laurell, “Bright, single-spatial-mode source of frequency non-degenerate, polarization-entangled photon pairs using periodically poled KTP,” Opt. Express 12, 3573–3580 (2004).
[Crossref] [PubMed]

M. Fiorentino, G. Messin, C.E. Kuklewicz, F.N.C. Wong, and J.H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[Crossref]

2003 (3)

Y.-H. Kim, S.P. Kulik, M.V. Chekhova, W.P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301 (2003).
[Crossref]

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

Y.-H. Kim, “Measurement of one-photon and two-photon wave packets in spontaneous parametric downconversion,” J. Opt. Soc. Am. B 20, 1959 (2003).
[Crossref]

2002 (1)

Y.-H. Kim and W.P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[Crossref]

2001 (5)

Y.-H. Kim, S.P. Kulik, and Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A 63, 060301 (2001).
[Crossref]

Y.-H. Kim, M.V. Chekova, S.P. Kulick, M.H. Rubin, and Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion,” Phys. Rev. A 63, 062301 (2001).
[Crossref]

Y.-H. Kim, S.P. Kulik, M.H. Rubin, and Y. Shih, “Comment on “Dispersion-independent high-visibility quantum interference in ultrafast parametric down-conversion,” Phys. Rev. Lett. 86, 4710 (2001).
[Crossref]

Y.-H. Kim, V. Berardi, M.V. Chekhova, and Y. Shih, “Anticorrelation effect in femtosecond-pulse pumped type-II spontaneous parametric down-conversion,” Phys. Rev. A 64, 011801 (2001).
[Crossref]

S. Takeuchi, “Beamlike twin-photon generation by use of type II parametric downconversion,” Opt. Lett. 26, 843–845 (2001).
[Crossref]

2000 (1)

Y.-H. Kim, S.P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802 (2000).
[Crossref]

1999 (2)

A.V. Sergienko, M. Atature, Z. Walton, G. Zjaeger, B.E.A. Saleh, and M.C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622 (1999).
[Crossref]

P.G. Kwiat, E. Waks, A.G. White, I. Appelbaum, and P.H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

1997 (2)

T.E. Keller and M.H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[Crossref]

W.P. Grice and I.A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[Crossref]

1996 (1)

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

1988 (1)

Y.H. Shih and C.O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[Crossref] [PubMed]

Agafonov, I.N.

T.Sh. Iskhakov, I.N. Agafonov, M.V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 105 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

Alley, C.O.

Y.H. Shih and C.O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[Crossref] [PubMed]

Appelbaum, I.

P.G. Kwiat, E. Waks, A.G. White, I. Appelbaum, and P.H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

Atature, M.

A.V. Sergienko, M. Atature, Z. Walton, G. Zjaeger, B.E.A. Saleh, and M.C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622 (1999).
[Crossref]

Baek, S.-Y.

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-Resolution Mode-Spacing Measurement of the Blue-Violet Diode Laser Using Interference of Felds Created with Time Delays Greater than the Coherence Time,” Jpn. J. Appl. Phys. 46, 7720–7723 (2007).
[Crossref]

Barz, S.

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photon. 4, 553–556 (2010).
[Crossref]

Beausoleil, R.G.

Bennink, R.S.

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

Berardi, V.

Y.-H. Kim, V. Berardi, M.V. Chekhova, and Y. Shih, “Anticorrelation effect in femtosecond-pulse pumped type-II spontaneous parametric down-conversion,” Phys. Rev. A 64, 011801 (2001).
[Crossref]

Bounouar, S.

M. Muller, S. Bounouar, K.D. Jons, M. Glassl, and P. Michler, “On-demand generation of indistinguishable polarization-entangled photon pairs,” Nat. Photon. 8, 224 (2014).
[Crossref]

Canalias, C.

Chekhova, M.V.

T.Sh. Iskhakov, I.N. Agafonov, M.V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 105 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

Y.-H. Kim, S.P. Kulik, M.V. Chekhova, W.P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301 (2003).
[Crossref]

Y.-H. Kim, V. Berardi, M.V. Chekhova, and Y. Shih, “Anticorrelation effect in femtosecond-pulse pumped type-II spontaneous parametric down-conversion,” Phys. Rev. A 64, 011801 (2001).
[Crossref]

Chekova, M.V.

Y.-H. Kim, M.V. Chekova, S.P. Kulick, M.H. Rubin, and Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion,” Phys. Rev. A 63, 062301 (2001).
[Crossref]

Chen, P.

H.-P. Lo, A. Yabushita, C.-W. Luo, P. Chen, and T. Kobayashi, “Beamlike photon-pair generation for two-photon interference and polarization entanglement,” Phys. Rev. A 83, 022313 (2011).
[Crossref]

Cronenberg, G.

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photon. 4, 553–556 (2010).
[Crossref]

Danila, O.

F. Kaiser, A. Issautier, L.A. Ngah, O. Danila, H. Herrmann, W. Sohler, A. Martin, and S. Tanzilli, “High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels,” New J. Phys. 14085015 (2012).
[Crossref]

Dimastrodonato, V.

G. Juska, V. Dimastrodonato, L.O. Mereni, A. Gocalinska, and E. Pelucchi, “Towards quantum-dot arrays of entangled photon emitters,” Nat. Photon. 7, 527 (2013).
[Crossref]

Du, S.

K. Liao, H. Yan, J. He, S. Du, Z.-M. Zhang, and S.-L. Zhu, “Subnatural-linewidth polarization-entangled photon pairs with controllable temporal with controllable temporal length,” Phys. Rev. Lett. 112, 243602 (2014).
[Crossref]

Eberhard, P.H.

P.G. Kwiat, E. Waks, A.G. White, I. Appelbaum, and P.H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

Evans, P.G.

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

Fedrizzi, A.

Fiorentino, M.

M. Fiorentino and R.G. Beausoleil, “Compact sources of polarization-entangled photons,” Opt. Express 16, 20149–20156 (2008).
[Crossref] [PubMed]

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]

M. Fiorentino, C.E. Kuklewicz, and F.N.C. Wong, “Source of polarization entanglement in a single periodically poled KTiOPO4 crystal with overlapping emission cones,” Opt. Express 13, 127–135 (2005).
[Crossref] [PubMed]

M. Fiorentino, G. Messin, C.E. Kuklewicz, F.N.C. Wong, and J.H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[Crossref]

Fragemann, A.

Gilaberte, M.

Glassl, M.

M. Muller, S. Bounouar, K.D. Jons, M. Glassl, and P. Michler, “On-demand generation of indistinguishable polarization-entangled photon pairs,” Nat. Photon. 8, 224 (2014).
[Crossref]

Gocalinska, A.

G. Juska, V. Dimastrodonato, L.O. Mereni, A. Gocalinska, and E. Pelucchi, “Towards quantum-dot arrays of entangled photon emitters,” Nat. Photon. 7, 527 (2013).
[Crossref]

Goggin, M.

Grabher, S.

Grice, W.P.

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

Y.-H. Kim, S.P. Kulik, M.V. Chekhova, W.P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301 (2003).
[Crossref]

Y.-H. Kim and W.P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[Crossref]

W.P. Grice and I.A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[Crossref]

Guo, G.-C.

He, J.

K. Liao, H. Yan, J. He, S. Du, Z.-M. Zhang, and S.-L. Zhu, “Subnatural-linewidth polarization-entangled photon pairs with controllable temporal with controllable temporal length,” Phys. Rev. Lett. 112, 243602 (2014).
[Crossref]

Hentschel, M.

Herbst, T.

Herrmann, H.

F. Kaiser, A. Issautier, L.A. Ngah, O. Danila, H. Herrmann, W. Sohler, A. Martin, and S. Tanzilli, “High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels,” New J. Phys. 14085015 (2012).
[Crossref]

Huang, Y.-F.

Hübel, H.

Humble, T.S.

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

Iskhakov, T.Sh.

T.Sh. Iskhakov, I.N. Agafonov, M.V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 105 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

Issautier, A.

F. Kaiser, A. Issautier, L.A. Ngah, O. Danila, H. Herrmann, W. Sohler, A. Martin, and S. Tanzilli, “High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels,” New J. Phys. 14085015 (2012).
[Crossref]

Jennewein, T.

Jofre, M.

Jons, K.D.

M. Muller, S. Bounouar, K.D. Jons, M. Glassl, and P. Michler, “On-demand generation of indistinguishable polarization-entangled photon pairs,” Nat. Photon. 8, 224 (2014).
[Crossref]

Juska, G.

G. Juska, V. Dimastrodonato, L.O. Mereni, A. Gocalinska, and E. Pelucchi, “Towards quantum-dot arrays of entangled photon emitters,” Nat. Photon. 7, 527 (2013).
[Crossref]

Kaiser, F.

F. Kaiser, A. Issautier, L.A. Ngah, O. Danila, H. Herrmann, W. Sohler, A. Martin, and S. Tanzilli, “High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels,” New J. Phys. 14085015 (2012).
[Crossref]

Karlsson, A.

Keller, T.E.

T.E. Keller and M.H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[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.

O. Kwon, K.-K. Park, Y.-S. Ra, Y.-S. Kim, and Y.-H. Kim, “Time-bin entangled photon pairs from spontaneous parametric down-conversion pumped by a cw multi-mode diode laser,” Opt. Express 21, 25492–25500 (2013).
[Crossref] [PubMed]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0⟩ + | 0,N⟩ state,” Phys. Rev. A 81, 063801 (2010).
[Crossref]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser,” Opt. Express 17, 13059–13069 (2009).
[Crossref] [PubMed]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-Resolution Mode-Spacing Measurement of the Blue-Violet Diode Laser Using Interference of Felds Created with Time Delays Greater than the Coherence Time,” Jpn. J. Appl. Phys. 46, 7720–7723 (2007).
[Crossref]

Y.-H. Kim, “Measurement of one-photon and two-photon wave packets in spontaneous parametric downconversion,” J. Opt. Soc. Am. B 20, 1959 (2003).
[Crossref]

Y.-H. Kim, S.P. Kulik, M.V. Chekhova, W.P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301 (2003).
[Crossref]

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

Y.-H. Kim and W.P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[Crossref]

Y.-H. Kim, S.P. Kulik, and Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A 63, 060301 (2001).
[Crossref]

Y.-H. Kim, M.V. Chekova, S.P. Kulick, M.H. Rubin, and Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion,” Phys. Rev. A 63, 062301 (2001).
[Crossref]

Y.-H. Kim, S.P. Kulik, M.H. Rubin, and Y. Shih, “Comment on “Dispersion-independent high-visibility quantum interference in ultrafast parametric down-conversion,” Phys. Rev. Lett. 86, 4710 (2001).
[Crossref]

Y.-H. Kim, V. Berardi, M.V. Chekhova, and Y. Shih, “Anticorrelation effect in femtosecond-pulse pumped type-II spontaneous parametric down-conversion,” Phys. Rev. A 64, 011801 (2001).
[Crossref]

Y.-H. Kim, S.P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802 (2000).
[Crossref]

Kim, Y.-S.

Kobayashi, T.

H.-P. Lo, A. Yabushita, C.-W. Luo, P. Chen, and T. Kobayashi, “Beamlike photon-pair generation for two-photon interference and polarization entanglement,” Phys. Rev. A 83, 022313 (2011).
[Crossref]

Kuklewicz, C.E.

M. Fiorentino, C.E. Kuklewicz, and F.N.C. Wong, “Source of polarization entanglement in a single periodically poled KTiOPO4 crystal with overlapping emission cones,” Opt. Express 13, 127–135 (2005).
[Crossref] [PubMed]

M. Fiorentino, G. Messin, C.E. Kuklewicz, F.N.C. Wong, and J.H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[Crossref]

Kulick, S.P.

Y.-H. Kim, M.V. Chekova, S.P. Kulick, M.H. Rubin, and Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion,” Phys. Rev. A 63, 062301 (2001).
[Crossref]

Kulik, S.P.

Y.-H. Kim, S.P. Kulik, M.V. Chekhova, W.P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301 (2003).
[Crossref]

Y.-H. Kim, S.P. Kulik, and Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A 63, 060301 (2001).
[Crossref]

Y.-H. Kim, S.P. Kulik, M.H. Rubin, and Y. Shih, “Comment on “Dispersion-independent high-visibility quantum interference in ultrafast parametric down-conversion,” Phys. Rev. Lett. 86, 4710 (2001).
[Crossref]

Y.-H. Kim, S.P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802 (2000).
[Crossref]

Kuzucu, O.

O. Kuzucu and F.N.C. Wong, “Pulsed Sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77, 032314 (2008).
[Crossref]

Kwiat, P.

Kwiat, P.G.

P.G. Kwiat, E. Waks, A.G. White, I. Appelbaum, and P.H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[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, 4337–4341 (1995).
[Crossref] [PubMed]

Kwon, O.

O. Kwon, K.-K. Park, Y.-S. Ra, Y.-S. Kim, and Y.-H. Kim, “Time-bin entangled photon pairs from spontaneous parametric down-conversion pumped by a cw multi-mode diode laser,” Opt. Express 21, 25492–25500 (2013).
[Crossref] [PubMed]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0⟩ + | 0,N⟩ state,” Phys. Rev. A 81, 063801 (2010).
[Crossref]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser,” Opt. Express 17, 13059–13069 (2009).
[Crossref] [PubMed]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-Resolution Mode-Spacing Measurement of the Blue-Violet Diode Laser Using Interference of Felds Created with Time Delays Greater than the Coherence Time,” Jpn. J. Appl. Phys. 46, 7720–7723 (2007).
[Crossref]

Laurell, F.

Leuchs, G.

T.Sh. Iskhakov, I.N. Agafonov, M.V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 105 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

Liao, K.

K. Liao, H. Yan, J. He, S. Du, Z.-M. Zhang, and S.-L. Zhu, “Subnatural-linewidth polarization-entangled photon pairs with controllable temporal with controllable temporal length,” Phys. Rev. Lett. 112, 243602 (2014).
[Crossref]

Ljunggren, D.

Lo, H.-P.

H.-P. Lo, A. Yabushita, C.-W. Luo, P. Chen, and T. Kobayashi, “Beamlike photon-pair generation for two-photon interference and polarization entanglement,” Phys. Rev. A 83, 022313 (2011).
[Crossref]

Luo, C.-W.

H.-P. Lo, A. Yabushita, C.-W. Luo, P. Chen, and T. Kobayashi, “Beamlike photon-pair generation for two-photon interference and polarization entanglement,” Phys. Rev. A 83, 022313 (2011).
[Crossref]

Marsden, P.

Martin, A.

F. Kaiser, A. Issautier, L.A. Ngah, O. Danila, H. Herrmann, W. Sohler, A. Martin, and S. Tanzilli, “High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels,” New J. Phys. 14085015 (2012).
[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]

Mereni, L.O.

G. Juska, V. Dimastrodonato, L.O. Mereni, A. Gocalinska, and E. Pelucchi, “Towards quantum-dot arrays of entangled photon emitters,” Nat. Photon. 7, 527 (2013).
[Crossref]

Messin, G.

M. Fiorentino, G. Messin, C.E. Kuklewicz, F.N.C. Wong, and J.H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[Crossref]

Michler, P.

M. Muller, S. Bounouar, K.D. Jons, M. Glassl, and P. Michler, “On-demand generation of indistinguishable polarization-entangled photon pairs,” Nat. Photon. 8, 224 (2014).
[Crossref]

Mitchell, M.W.

Muller, M.

M. Muller, S. Bounouar, K.D. Jons, M. Glassl, and P. Michler, “On-demand generation of indistinguishable polarization-entangled photon pairs,” Nat. Photon. 8, 224 (2014).
[Crossref]

Ngah, L.A.

F. Kaiser, A. Issautier, L.A. Ngah, O. Danila, H. Herrmann, W. Sohler, A. Martin, and S. Tanzilli, “High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels,” New J. Phys. 14085015 (2012).
[Crossref]

Niu, X.-L.

Ou, Z.Y.

Park, K.-K.

Pelton, M.

Pelucchi, E.

G. Juska, V. Dimastrodonato, L.O. Mereni, A. Gocalinska, and E. Pelucchi, “Towards quantum-dot arrays of entangled photon emitters,” Nat. Photon. 7, 527 (2013).
[Crossref]

Perez, D.

Poppe, A.

Predojevic, A.

Pruneri, V.

Ra, Y.-S.

Ramelow, S.

Rangarajan, R.

Rarity, J.

Rubin, M. H.

Rubin, M.H.

Y.-H. Kim, S.P. Kulik, M.H. Rubin, and Y. Shih, “Comment on “Dispersion-independent high-visibility quantum interference in ultrafast parametric down-conversion,” Phys. Rev. Lett. 86, 4710 (2001).
[Crossref]

Y.-H. Kim, M.V. Chekova, S.P. Kulick, M.H. Rubin, and Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion,” Phys. Rev. A 63, 062301 (2001).
[Crossref]

T.E. Keller and M.H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[Crossref]

Saleh, B.E.A.

A.V. Sergienko, M. Atature, Z. Walton, G. Zjaeger, B.E.A. Saleh, and M.C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622 (1999).
[Crossref]

Sergienko, A. V.

Sergienko, A.V.

A.V. Sergienko, M. Atature, Z. Walton, G. Zjaeger, B.E.A. Saleh, and M.C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622 (1999).
[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, 4337–4341 (1995).
[Crossref] [PubMed]

Shapiro, J.H.

M. Fiorentino, G. Messin, C.E. Kuklewicz, F.N.C. Wong, and J.H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[Crossref]

Shih, Y.

Y.-H. Kim, S.P. Kulik, M.V. Chekhova, W.P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301 (2003).
[Crossref]

Y.-H. Kim, S.P. Kulik, and Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A 63, 060301 (2001).
[Crossref]

Y.-H. Kim, M.V. Chekova, S.P. Kulick, M.H. Rubin, and Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion,” Phys. Rev. A 63, 062301 (2001).
[Crossref]

Y.-H. Kim, S.P. Kulik, M.H. Rubin, and Y. Shih, “Comment on “Dispersion-independent high-visibility quantum interference in ultrafast parametric down-conversion,” Phys. Rev. Lett. 86, 4710 (2001).
[Crossref]

Y.-H. Kim, V. Berardi, M.V. Chekhova, and Y. Shih, “Anticorrelation effect in femtosecond-pulse pumped type-II spontaneous parametric down-conversion,” Phys. Rev. A 64, 011801 (2001).
[Crossref]

Y.-H. Kim, S.P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802 (2000).
[Crossref]

A. V. Sergienko, Y. Shih, and M. H. Rubin, “Experimental evaluation of a two-photon wave packet in type-II parametric downconversion,” J. Opt. Soc. Am. B 12, 859 (1996).
[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, 4337–4341 (1995).
[Crossref] [PubMed]

Shih, Y.H.

Y.H. Shih and C.O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[Crossref] [PubMed]

Sohler, W.

F. Kaiser, A. Issautier, L.A. Ngah, O. Danila, H. Herrmann, W. Sohler, A. Martin, and S. Tanzilli, “High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels,” New J. Phys. 14085015 (2012).
[Crossref]

Steinlechner, F.

Takeuchi, S.

Tanzilli, S.

F. Kaiser, A. Issautier, L.A. Ngah, O. Danila, H. Herrmann, W. Sohler, A. Martin, and S. Tanzilli, “High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels,” New J. Phys. 14085015 (2012).
[Crossref]

Teich, M.C.

A.V. Sergienko, M. Atature, Z. Walton, G. Zjaeger, B.E.A. Saleh, and M.C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622 (1999).
[Crossref]

Tengner, M.

Torres, J.P.

Trojek, P.

Ursin, R.

Waks, E.

P.G. Kwiat, E. Waks, A.G. White, I. Appelbaum, and P.H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

Walmsley, I.A.

W.P. Grice and I.A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[Crossref]

Walther, P.

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photon. 4, 553–556 (2010).
[Crossref]

Walton, Z.

A.V. Sergienko, M. Atature, Z. Walton, G. Zjaeger, B.E.A. Saleh, and M.C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622 (1999).
[Crossref]

Weier, H.

Weihs, G.

Weinfurter, H.

F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M.W. Mitchell, J.P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express 20, 9640–9649 (2012).
[Crossref] [PubMed]

P. Trojek and H. Weinfurter, “Collinear source of polarization-entangled photon pairs at nondegenerate wavelengths,” Appl. Phys. Lett. 92, 211103 (2008).
[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, 4337–4341 (1995).
[Crossref] [PubMed]

White, A.G.

P.G. Kwiat, E. Waks, A.G. White, I. Appelbaum, and P.H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

Wong, F.N.C.

O. Kuzucu and F.N.C. Wong, “Pulsed Sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77, 032314 (2008).
[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]

M. Fiorentino, C.E. Kuklewicz, and F.N.C. Wong, “Source of polarization entanglement in a single periodically poled KTiOPO4 crystal with overlapping emission cones,” Opt. Express 13, 127–135 (2005).
[Crossref] [PubMed]

M. Fiorentino, G. Messin, C.E. Kuklewicz, F.N.C. Wong, and J.H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[Crossref]

Xiang, G.-Y.

Yabushita, A.

H.-P. Lo, A. Yabushita, C.-W. Luo, P. Chen, and T. Kobayashi, “Beamlike photon-pair generation for two-photon interference and polarization entanglement,” Phys. Rev. A 83, 022313 (2011).
[Crossref]

Yan, H.

K. Liao, H. Yan, J. He, S. Du, Z.-M. Zhang, and S.-L. Zhu, “Subnatural-linewidth polarization-entangled photon pairs with controllable temporal with controllable temporal length,” Phys. Rev. Lett. 112, 243602 (2014).
[Crossref]

Zeilinger, A.

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photon. 4, 553–556 (2010).
[Crossref]

M. Hentschel, H. Hübel, A. Poppe, and A. Zeilinger, “Three-color Sagnac source of polarization-entangled photon pairs,” Opt. Express 17, 23153–23159 (2009).
[Crossref]

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15, 15377–15386 (2007).
[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]

Zhang, Z.-M.

K. Liao, H. Yan, J. He, S. Du, Z.-M. Zhang, and S.-L. Zhu, “Subnatural-linewidth polarization-entangled photon pairs with controllable temporal with controllable temporal length,” Phys. Rev. Lett. 112, 243602 (2014).
[Crossref]

Zhu, S.-L.

K. Liao, H. Yan, J. He, S. Du, Z.-M. Zhang, and S.-L. Zhu, “Subnatural-linewidth polarization-entangled photon pairs with controllable temporal with controllable temporal length,” Phys. Rev. Lett. 112, 243602 (2014).
[Crossref]

Zjaeger, G.

A.V. Sergienko, M. Atature, Z. Walton, G. Zjaeger, B.E.A. Saleh, and M.C. Teich, “Quantum cryptography using femtosecond-pulsed parametric down-conversion,” Phys. Rev. A 60, R2622 (1999).
[Crossref]

Appl. Phys. Lett. (1)

P. Trojek and H. Weinfurter, “Collinear source of polarization-entangled photon pairs at nondegenerate wavelengths,” Appl. Phys. Lett. 92, 211103 (2008).
[Crossref]

J. Mod. Opt. (1)

Y.-H. Kim and W.P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[Crossref]

J. Opt. Soc. Am. B (2)

Jpn. J. Appl. Phys. (1)

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-Resolution Mode-Spacing Measurement of the Blue-Violet Diode Laser Using Interference of Felds Created with Time Delays Greater than the Coherence Time,” Jpn. J. Appl. Phys. 46, 7720–7723 (2007).
[Crossref]

Nat. Photon. (3)

G. Juska, V. Dimastrodonato, L.O. Mereni, A. Gocalinska, and E. Pelucchi, “Towards quantum-dot arrays of entangled photon emitters,” Nat. Photon. 7, 527 (2013).
[Crossref]

M. Muller, S. Bounouar, K.D. Jons, M. Glassl, and P. Michler, “On-demand generation of indistinguishable polarization-entangled photon pairs,” Nat. Photon. 8, 224 (2014).
[Crossref]

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photon. 4, 553–556 (2010).
[Crossref]

New J. Phys. (1)

F. Kaiser, A. Issautier, L.A. Ngah, O. Danila, H. Herrmann, W. Sohler, A. Martin, and S. Tanzilli, “High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels,” New J. Phys. 14085015 (2012).
[Crossref]

Opt. Express (11)

R. Rangarajan, M. Goggin, and P. Kwiat, “Optimizing type-I polarization-entangled photons,” Opt. Express 17, 18920–18933 (2009).
[Crossref]

M. Pelton, P. Marsden, D. Ljunggren, M. Tengner, A. Karlsson, A. Fragemann, C. Canalias, and F. Laurell, “Bright, single-spatial-mode source of frequency non-degenerate, polarization-entangled photon pairs using periodically poled KTP,” Opt. Express 12, 3573–3580 (2004).
[Crossref] [PubMed]

F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M.W. Mitchell, J.P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express 20, 9640–9649 (2012).
[Crossref] [PubMed]

M. Fiorentino, C.E. Kuklewicz, and F.N.C. Wong, “Source of polarization entanglement in a single periodically poled KTiOPO4 crystal with overlapping emission cones,” Opt. Express 13, 127–135 (2005).
[Crossref] [PubMed]

F. Steinlechner, S. Ramelow, M. Jofre, M. Gilaberte, T. Jennewein, J.P. Torres, M.W. Mitchell, and V. Pruneri, “Phase-stable source of polarization-entangled photons in a linear double-pass configuration,” Opt. Express 21, 11943–19951 (2013).
[Crossref] [PubMed]

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15, 15377–15386 (2007).
[Crossref] [PubMed]

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[Crossref]

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[Crossref] [PubMed]

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Opt. Lett. (2)

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[Crossref]

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[Crossref]

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Figures (3)

Fig. 1
Fig. 1

Experimental schematic for the bright source of polarization-entangled photon pairs based on the “universal Bell-state synthesizer” scheme by using a 10 mm type-II PPKTP pumped by a broadband cw multi-mode diode laser. (a) Non-collinear type-II SPDC is used so that the signal (e-ray) and the idler (o-ray) photons emerge from the PPKTP crystal in overlapping concentric rings. Two conjugate path modes 1 and 2 (marked by small circles) were selected. (b) The signal and idler photons, after making their polarization state identical by using a half-wave plate (HWP), are made to overlap at the polarizing beam splitter (PBS) by a trombone prism (T) and collimated by collimation lenses (L1, L2). (c) The detection part consists of single photon detectors (D1, D2) and polarization analyzers (P1, P2).

Fig. 2
Fig. 2

Experimental data showing high-visibility two-photon quantum interference when (a) single-mode fiber coupled detectors are used and (b) multi-mode fiber coupled detectors are used. The inset shows the settings of the polarization analyzers P1 and P2. The visibilities are 0.978 for (a) and 0.936 for (b). The solid lines are curves due to Eq. (15), obtained by summing up the effect of 50 most dominant modes of multi-mode diode laser with 0.015nm mode spacing. The best fitting is obtained when the PPKTP temperature is set at 79.6°C although the measured temperature is 86.8°C. This discrepancy is due to systematic errors in the temperature measurement (as the location of the thermocouple in our setup was a bit far from the PPKTP crystal).

Fig. 3
Fig. 3

The reconstructed density matrix of the generated Bell state. The entangled state with respect to 1 2 ( | H , H + | V , V ) has fidelity 0.992 and 0.968 for photon pairs coupled into (a) single-mode fibers and (b) multi-mode fibers for detection. Concurrence, which quantifies the amount of two-qubit entanglement, is for (a) 0.983 and for (b) 0.937.

Equations (18)

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1 2 ( | H 1 , V 2 V 2 , H 1 | + | V 1 , H 2 H 2 , V 1 | ) ,
1 2 ( | H , H + | V , V ) .
ρ = d ω p S ( ω p ) | | ψ ( ω p ) ψ ( ω p ) | .
S ( ω p ) = n = N N S 0 ( ω p ) δ ( ω p ω p 0 n Δ ω p ) n = N N S 0 ( ω p 0 + n Δ ω p ) ,
S 0 ( ω p ) exp ( ( ω p ω p 0 ) 2 / δ ω p 2 ) ,
| ψ ( ω p ) ~ d k o d k e 0 L d z e i Δ z δ ( ω o + ω e ω p ) × [ a ^ 1 H ( ω e ) a ^ 2 V ( ω o ) + a ^ 2 H ( ω e ) a ^ 1 V ( ω o ) ] | 0 ,
Δ = k p k e k o 2 π / Λ ,
Δ = Δ 0 ( ω p Ω p ) D + 1 2 ( ω o ω e ) D ,
Δ 0 = K p K e K o 2 π / Λ
D + = [ 1 u o ( Ω o ) + 1 u o ( Ω e ) ] 1 u o ( Ω p ) ,
D = 1 u o ( Ω o ) 1 u e ( Ω e ) ,
R c d t 1 d t 2 tr [ ρ E 1 ( ) ( t 1 ) E 2 ( ) ( t 2 ) E 2 ( + ) ( t 2 ) E 1 ( + ) ( t 1 ) ] ,
E 1 ( + ) ( t 1 ) = 1 2 d ω [ a ^ 1 H ( ω ) + e i ω τ a ^ 2 V ( ω ) ] e i ω t 1
E 1 ( + ) ( t 2 ) = 1 2 d ω [ a ^ 1 V ( ω ) ± e i ω τ a ^ 2 H ( ω ) ] e i ω t 2
R c = 1 ± T ( τ )
T ( τ ) = d ω p S ( ω p ) cos [ { 2 D + D ( ω p 0 ω p ) + 2 Δ 0 D } τ ] tri ( 2 π L D τ ) .
tri ( x ) = max ( 1 x , 0 ) ,
2 D + D ( ω p 0 ω p ) + 2 Δ 0 D 2 π L D .

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