Abstract

It is shown that for a phase-matched nonlinear process producing entangled states, different Bell states are generated for different mismatch values. In particular, generation of the singlet Bell state is demonstrated within the natural linewidth of collinear frequency-degenerate type-II spontaneous parametric down-conversion (SPDC) without the o-e delay compensation. The singlet state can be filtered out by spectral selection or by the time selection of the two-photon amplitude at the output of a dispersive fibre. The effect is of considerable importance for fibre quantum communication.

© 2007 Optical Society of America

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References

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  1. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
    [CrossRef] [PubMed]
  2. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, "Ultrabright source of polarizationentangled photons," Phys. Rev. A 60, R773-R776 (1999).
    [CrossRef]
  3. G. Brida, M. Genovese, C. Novero, and E. Predazzi, "New experimental test of Bell inequalities by the use of a non-maximally entangled photon state," Phys. Lett. A 268, 12-16 (2000).
    [CrossRef]
  4. L. J. Wang, C. K. Hong, and S. R. Friberg, "Generation of correlated photons via four-wave mixing in optical fibres," J. Opt. B: Quantum and Semiclass. Opt. 3, 346-352 (2001).
    [CrossRef]
  5. J. E. Sharping, M. Fiorentino, and P. Kumar, "Observation of twin-beam-type quantum correlation in optical fiber," Opt. Lett. 26, 367369 (2001).
    [CrossRef]
  6. H. Takesue and K. Inoue, "Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop," Phys. Rev. A 70, 031802(R) (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. G. Brida, M. V. Chekhova, M. Genovese, and L. A. Krivitsky, submitted a manuscript called "Bell states generation within the SPDC phase-matching bandwidth."
  12. P. G. Kwiat, A. J. Berglund, J. B. Altepeter, A. G. White, "Experimental verification of decoherence-free subspaces," Science 290, 498-501 (2000).
    [CrossRef] [PubMed]
  13. K. Banaszek, A. Dragan, W. Wasilewski, and C. Radzewicz, "Experimental demonstration of entanglementenhanced classical communication over a quantum channel with correlated noise," Phys. Rev. Lett. 92, 257901 (2004).
    [CrossRef] [PubMed]
  14. S. Braunstein and A. Mann, "Measurement of the Bell operator and quantum teleportation," Phys. Rev. A 51, R1727-R1730 (1995).
    [CrossRef] [PubMed]
  15. M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, "Diagnosis, Prescription, and Prognosis of a Bell-State Filter by Quantum Process Tomography," Phys. Rev. Lett. 91, 120402 (2003).
    [CrossRef] [PubMed]
  16. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-578 (1997).
    [CrossRef]
  17. D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, "Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 80, 1121-1125 (1998).
    [CrossRef]
  18. A. V. Burlakov, S. P. Kulik, G. O. Rytikov, and M. V. Chekhova, "Biphoton light generation in polarizationfrequency bell states," JETP 95, 639-644 (2002).
    [CrossRef]
  19. V. P. Karassiov and A. V. Masalov, "Nonpolarized states of light in quantum optics," Opt. Spectrosc. 74, 928-936 (1993).
  20. Because in half of the cases both photons go to the same output, the state is produced with 50% probability.
  21. In this regime higher-order contributions are negligible as shown both from theoretical and experimental results, e.g. G. Zambra et al., Phys. Rev. Lett. 95, 063602 (2005).
    [CrossRef] [PubMed]
  22. G. Brida,M. V. Chekhova,M. Genovese,M. Gramegna, and L. A. Krivitsky, "Dispersion spreading of Biphotons in Optical Fibers and Two-Photon Interference," Phys. Rev. Lett. 96, 143601 (2006).
    [CrossRef] [PubMed]
  23. G. Brida, M. V. Chekhova, M. Genovese, and L. A. Krivitsky, "Interference structure of two-photon amplitude revealed by dispersion spreading," Phys. Rev. A 75, 015801 (2007).
    [CrossRef]

2007 (1)

G. Brida, M. V. Chekhova, M. Genovese, and L. A. Krivitsky, "Interference structure of two-photon amplitude revealed by dispersion spreading," Phys. Rev. A 75, 015801 (2007).
[CrossRef]

2006 (1)

G. Brida,M. V. Chekhova,M. Genovese,M. Gramegna, and L. A. Krivitsky, "Dispersion spreading of Biphotons in Optical Fibers and Two-Photon Interference," Phys. Rev. Lett. 96, 143601 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (1)

K. Banaszek, A. Dragan, W. Wasilewski, and C. Radzewicz, "Experimental demonstration of entanglementenhanced classical communication over a quantum channel with correlated noise," Phys. Rev. Lett. 92, 257901 (2004).
[CrossRef] [PubMed]

2003 (1)

M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, "Diagnosis, Prescription, and Prognosis of a Bell-State Filter by Quantum Process Tomography," Phys. Rev. Lett. 91, 120402 (2003).
[CrossRef] [PubMed]

2002 (1)

A. V. Burlakov, S. P. Kulik, G. O. Rytikov, and M. V. Chekhova, "Biphoton light generation in polarizationfrequency bell states," JETP 95, 639-644 (2002).
[CrossRef]

2001 (2)

L. J. Wang, C. K. Hong, and S. R. Friberg, "Generation of correlated photons via four-wave mixing in optical fibres," J. Opt. B: Quantum and Semiclass. Opt. 3, 346-352 (2001).
[CrossRef]

J. E. Sharping, M. Fiorentino, and P. Kumar, "Observation of twin-beam-type quantum correlation in optical fiber," Opt. Lett. 26, 367369 (2001).
[CrossRef]

2000 (2)

G. Brida, M. Genovese, C. Novero, and E. Predazzi, "New experimental test of Bell inequalities by the use of a non-maximally entangled photon state," Phys. Lett. A 268, 12-16 (2000).
[CrossRef]

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, A. G. White, "Experimental verification of decoherence-free subspaces," Science 290, 498-501 (2000).
[CrossRef] [PubMed]

1999 (1)

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, "Ultrabright source of polarizationentangled photons," Phys. Rev. A 60, R773-R776 (1999).
[CrossRef]

1998 (1)

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, "Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 80, 1121-1125 (1998).
[CrossRef]

1997 (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-578 (1997).
[CrossRef]

1995 (2)

S. Braunstein and A. Mann, "Measurement of the Bell operator and quantum teleportation," Phys. Rev. A 51, R1727-R1730 (1995).
[CrossRef] [PubMed]

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

1993 (1)

V. P. Karassiov and A. V. Masalov, "Nonpolarized states of light in quantum optics," Opt. Spectrosc. 74, 928-936 (1993).

J. Opt. B: Quantum and Semiclass. Opt. (1)

L. J. Wang, C. K. Hong, and S. R. Friberg, "Generation of correlated photons via four-wave mixing in optical fibres," J. Opt. B: Quantum and Semiclass. Opt. 3, 346-352 (2001).
[CrossRef]

JETP (1)

A. V. Burlakov, S. P. Kulik, G. O. Rytikov, and M. V. Chekhova, "Biphoton light generation in polarizationfrequency bell states," JETP 95, 639-644 (2002).
[CrossRef]

Nature (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-578 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

J. E. Sharping, M. Fiorentino, and P. Kumar, "Observation of twin-beam-type quantum correlation in optical fiber," Opt. Lett. 26, 367369 (2001).
[CrossRef]

Opt. Spectrosc. (1)

V. P. Karassiov and A. V. Masalov, "Nonpolarized states of light in quantum optics," Opt. Spectrosc. 74, 928-936 (1993).

Phys. Lett. A (1)

G. Brida, M. Genovese, C. Novero, and E. Predazzi, "New experimental test of Bell inequalities by the use of a non-maximally entangled photon state," Phys. Lett. A 268, 12-16 (2000).
[CrossRef]

Phys. Rep (1)

M. Genovese, "Research on hidden variable theories: A review of recent progresses," Phys. Rep.  413, 319-396 (2005).
[CrossRef]

Phys. Rev. A (3)

S. Braunstein and A. Mann, "Measurement of the Bell operator and quantum teleportation," Phys. Rev. A 51, R1727-R1730 (1995).
[CrossRef] [PubMed]

G. Brida, M. V. Chekhova, M. Genovese, and L. A. Krivitsky, "Interference structure of two-photon amplitude revealed by dispersion spreading," Phys. Rev. A 75, 015801 (2007).
[CrossRef]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, "Ultrabright source of polarizationentangled photons," Phys. Rev. A 60, R773-R776 (1999).
[CrossRef]

Phys. Rev. Lett. (5)

G. Brida,M. V. Chekhova,M. Genovese,M. Gramegna, and L. A. Krivitsky, "Dispersion spreading of Biphotons in Optical Fibers and Two-Photon Interference," Phys. Rev. Lett. 96, 143601 (2006).
[CrossRef] [PubMed]

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

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, "Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 80, 1121-1125 (1998).
[CrossRef]

M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, "Diagnosis, Prescription, and Prognosis of a Bell-State Filter by Quantum Process Tomography," Phys. Rev. Lett. 91, 120402 (2003).
[CrossRef] [PubMed]

K. Banaszek, A. Dragan, W. Wasilewski, and C. Radzewicz, "Experimental demonstration of entanglementenhanced classical communication over a quantum channel with correlated noise," Phys. Rev. Lett. 92, 257901 (2004).
[CrossRef] [PubMed]

Science (1)

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, A. G. White, "Experimental verification of decoherence-free subspaces," Science 290, 498-501 (2000).
[CrossRef] [PubMed]

Other (6)

D. N. Klyshko, Photons and Nonlinear Optics (Gordon and Breach, New York, 1988).

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

G. Brida, M. V. Chekhova, M. Genovese, and L. A. Krivitsky, submitted a manuscript called "Bell states generation within the SPDC phase-matching bandwidth."

Because in half of the cases both photons go to the same output, the state is produced with 50% probability.

In this regime higher-order contributions are negligible as shown both from theoretical and experimental results, e.g. G. Zambra et al., Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

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

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup. A type-II BBO crystal is cut for collinear frequency-degenerate phasematching; P1 and P2, Glan prisms; D1, D2, single-photon counting modules. Retardation plates (QWP and HWP) are used to study the invariance of the Bell state |Ψ-〉 under polarization transformations. In some measurements, the monochromator is replaced by a 1 km single-mode fibre inserted after the crystal.

Fig. 2.
Fig. 2.

(a) Theoretical dependence of the coincidences counting rate on the frequency Ω for various orientations θ 2 of the Glan prism in channel 2. The Glan prism in channel 1 is fixed at θ 1=45°. (b) Experimental dependence of the coincidence counting rate on the wavelength selected by the monochromator for two cases: θ 1=θ 2=45° (squares, solid line, in black) and θ 1=45°,θ 2=-45° (triangles, dashed line, in red). Lines represent a fit with Eq.(4).

Fig. 3.
Fig. 3.

Polarization interference fringes for the singlet Bell state |Ψ;-〉 (the selected wavelength is λ=708.5nm).

Fig. 4.
Fig. 4.

Experimental dependence of the coincidence counting rate on the wavelength selected by the monochromator for the following orientations of the HWP placed after the crystal: 7°(circles, dotted line, in red); 17° (squares, dashed line, in green); 22,5° (triangles, solid line, in black). Orientations of the Glan prisms are 45°,45° (a) and 45°,-45° (b). Dashed vertical bars show the wavelength where |Ψ-〉 is generated. Lines represent the theoretical fit.

Fig. 5.
Fig. 5.

Experimental dependence of the coincidence counting rate on the delay between the arrivals of two photons, with the monochromator replaced by a 1 km optical fibre, for 45°,45° (triangles in black) and 45°,-45° (circles in red) settings of the Glan prisms.

Equations (6)

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Ψ = d 3 k d 3 k , d 3 r F NL ( r ) e i Δ ( k , k , ) r a P , k a P , k , vac ,
Ψ = d δ F NL ( δ ) { e i δ P 1 , P 2 + e i δ P 3 , P 4 } ,
Ψ = d Ω F ( Ω ) [ a H ( ω 0 + Ω ) a V ( ω 0 Ω ) e i Ω τ 0
+ a V ( ω 0 + Ω ) a H ( ω 0 Ω ) e i Ω τ 0 ] vac ,
R c = sin 2 ( Ω τ 0 ) ( Ω τ 0 ) 2 [ sin 2 ( θ 1 + θ 2 ) cos 2 ( Ω τ 0 )
+ sin 2 ( θ 1 θ 2 ) sin 2 ( Ω τ 0 ) ] .

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