Abstract

We address the generation of entangled photon pairs by parametric downconversion from solid state cw lasers with small coherence time. We consider a compact and low-cost setup based on a two-crystal scheme with type-I phase matching. We reconstruct the full density matrix by quantum tomography and analyze in detail the entanglement properties of the generated state as a function of the crystal’s length and the coherence time of the pump. We verify the possibility to improve the visibility using a purification protocol based on a compensation crystal.

© 2008 Optical Society of America

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  1. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773-R776 (1999).
    [CrossRef]
  2. D. Dehlinger and M. W. Mitchell, “Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory,” Am. J. Phys. 70, 903-910 (2002).
    [CrossRef]
  3. Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, “Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond laser pulses,” Phys. Rev. A 66, 033816 (2002)
    [CrossRef]
  4. M.G. A.Paris and J.Rehacek, eds., “Quantum state estimation,” Lect. Notes Phys. 649, 1-4 (2004).
  5. G. M. D'Ariano, L. Maccone, and M. G. A. Paris, “Quorum of observables for universal quantum estimation,” J. Phys. A 34, 93-104 (2001).
    [CrossRef]
  6. K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (2000).
    [CrossRef]
  7. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
    [CrossRef]
  8. A. Gogo, W. D. Snyder, and M. Beck, “Comparing quantum and classical correlations in a quantum eraser,” Phys. Rev. A 71, 052103 (2005).
    [CrossRef]
  9. M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122-5133(1994).
    [CrossRef] [PubMed]
  10. C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409-2418 (1985).
    [CrossRef] [PubMed]
  11. G. Brida, M. Chekhova, M. Genovese, and L. Krivitsky, “Generation of different bell state within spontaneous parametric down-conversion phase-matching bandwidth,” Phys. Rev. A 76, 053807 (2007)
    [CrossRef]
  12. G. Brida, M. V. Chekhova, M. Genovese, and L. A. Krivitsky, “Two-photon entanglement generation: different Bell states within the linewidth of phase-matching,” Opt. Express 15, 10182-10188 (2007)
    [CrossRef] [PubMed]
  13. A. V. Smith, SNLO nonlinear optics software, Sandia National Laboratories, http://www.sandia.gov/imrl/X1118/xxtal.htm.
  14. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003), pp. 69-120.
  15. A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: theory and experiment,” Phys. Rev. A 53, 4360-4371 (1996)
    [CrossRef] [PubMed]
  16. K. Blushs and M. Auzinsh, “Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation,” Phys. Rev. A 69, 063806 (2004).
    [CrossRef]

2007 (2)

G. Brida, M. Chekhova, M. Genovese, and L. Krivitsky, “Generation of different bell state within spontaneous parametric down-conversion phase-matching bandwidth,” Phys. Rev. A 76, 053807 (2007)
[CrossRef]

G. Brida, M. V. Chekhova, M. Genovese, and L. A. Krivitsky, “Two-photon entanglement generation: different Bell states within the linewidth of phase-matching,” Opt. Express 15, 10182-10188 (2007)
[CrossRef] [PubMed]

2005 (1)

A. Gogo, W. D. Snyder, and M. Beck, “Comparing quantum and classical correlations in a quantum eraser,” Phys. Rev. A 71, 052103 (2005).
[CrossRef]

2004 (1)

K. Blushs and M. Auzinsh, “Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation,” Phys. Rev. A 69, 063806 (2004).
[CrossRef]

2002 (2)

D. Dehlinger and M. W. Mitchell, “Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory,” Am. J. Phys. 70, 903-910 (2002).
[CrossRef]

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, “Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond laser pulses,” Phys. Rev. A 66, 033816 (2002)
[CrossRef]

2001 (2)

G. M. D'Ariano, L. Maccone, and M. G. A. Paris, “Quorum of observables for universal quantum estimation,” J. Phys. A 34, 93-104 (2001).
[CrossRef]

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

2000 (1)

K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (2000).
[CrossRef]

1999 (1)

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

1996 (1)

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: theory and experiment,” Phys. Rev. A 53, 4360-4371 (1996)
[CrossRef] [PubMed]

1994 (1)

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122-5133(1994).
[CrossRef] [PubMed]

1985 (1)

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409-2418 (1985).
[CrossRef] [PubMed]

Appelbaum, I.

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

Auzinsh, M.

K. Blushs and M. Auzinsh, “Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation,” Phys. Rev. A 69, 063806 (2004).
[CrossRef]

Banaszek, K.

K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (2000).
[CrossRef]

Beck, M.

A. Gogo, W. D. Snyder, and M. Beck, “Comparing quantum and classical correlations in a quantum eraser,” Phys. Rev. A 71, 052103 (2005).
[CrossRef]

Blushs, K.

K. Blushs and M. Auzinsh, “Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation,” Phys. Rev. A 69, 063806 (2004).
[CrossRef]

Brida, G.

G. Brida, M. V. Chekhova, M. Genovese, and L. A. Krivitsky, “Two-photon entanglement generation: different Bell states within the linewidth of phase-matching,” Opt. Express 15, 10182-10188 (2007)
[CrossRef] [PubMed]

G. Brida, M. Chekhova, M. Genovese, and L. Krivitsky, “Generation of different bell state within spontaneous parametric down-conversion phase-matching bandwidth,” Phys. Rev. A 76, 053807 (2007)
[CrossRef]

Chekhova, M.

G. Brida, M. Chekhova, M. Genovese, and L. Krivitsky, “Generation of different bell state within spontaneous parametric down-conversion phase-matching bandwidth,” Phys. Rev. A 76, 053807 (2007)
[CrossRef]

Chekhova, M. V.

D'Ariano, G. M.

G. M. D'Ariano, L. Maccone, and M. G. A. Paris, “Quorum of observables for universal quantum estimation,” J. Phys. A 34, 93-104 (2001).
[CrossRef]

K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (2000).
[CrossRef]

Dehlinger, D.

D. Dehlinger and M. W. Mitchell, “Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory,” Am. J. Phys. 70, 903-910 (2002).
[CrossRef]

Eberhard, P. G.

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

Genovese, M.

G. Brida, M. V. Chekhova, M. Genovese, and L. A. Krivitsky, “Two-photon entanglement generation: different Bell states within the linewidth of phase-matching,” Opt. Express 15, 10182-10188 (2007)
[CrossRef] [PubMed]

G. Brida, M. Chekhova, M. Genovese, and L. Krivitsky, “Generation of different bell state within spontaneous parametric down-conversion phase-matching bandwidth,” Phys. Rev. A 76, 053807 (2007)
[CrossRef]

Gogo, A.

A. Gogo, W. D. Snyder, and M. Beck, “Comparing quantum and classical correlations in a quantum eraser,” Phys. Rev. A 71, 052103 (2005).
[CrossRef]

Hong, C. K.

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409-2418 (1985).
[CrossRef] [PubMed]

James, D. F. V.

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

Joobeur, A.

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: theory and experiment,” Phys. Rev. A 53, 4360-4371 (1996)
[CrossRef] [PubMed]

Klyshko, D. N.

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122-5133(1994).
[CrossRef] [PubMed]

Krivitsky, L.

G. Brida, M. Chekhova, M. Genovese, and L. Krivitsky, “Generation of different bell state within spontaneous parametric down-conversion phase-matching bandwidth,” Phys. Rev. A 76, 053807 (2007)
[CrossRef]

Krivitsky, L. A.

Kwiat, P. G.

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

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

Larchuk, T. S.

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: theory and experiment,” Phys. Rev. A 53, 4360-4371 (1996)
[CrossRef] [PubMed]

Maccone, L.

G. M. D'Ariano, L. Maccone, and M. G. A. Paris, “Quorum of observables for universal quantum estimation,” J. Phys. A 34, 93-104 (2001).
[CrossRef]

Mandel, L.

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409-2418 (1985).
[CrossRef] [PubMed]

Matsumoto, K.

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, “Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond laser pulses,” Phys. Rev. A 66, 033816 (2002)
[CrossRef]

Mitchell, M. W.

D. Dehlinger and M. W. Mitchell, “Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory,” Am. J. Phys. 70, 903-910 (2002).
[CrossRef]

Munro, W. J.

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

Nakamura, K.

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, “Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond laser pulses,” Phys. Rev. A 66, 033816 (2002)
[CrossRef]

Nambu, Y.

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, “Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond laser pulses,” Phys. Rev. A 66, 033816 (2002)
[CrossRef]

Paris, M. G. A.

G. M. D'Ariano, L. Maccone, and M. G. A. Paris, “Quorum of observables for universal quantum estimation,” J. Phys. A 34, 93-104 (2001).
[CrossRef]

K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (2000).
[CrossRef]

Rubin, M. H.

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122-5133(1994).
[CrossRef] [PubMed]

Sacchi, M. F.

K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (2000).
[CrossRef]

Saleh, B. E. A.

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: theory and experiment,” Phys. Rev. A 53, 4360-4371 (1996)
[CrossRef] [PubMed]

Sergienko, A. V.

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122-5133(1994).
[CrossRef] [PubMed]

Shih, Y. H.

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122-5133(1994).
[CrossRef] [PubMed]

Smith, A. V.

A. V. Smith, SNLO nonlinear optics software, Sandia National Laboratories, http://www.sandia.gov/imrl/X1118/xxtal.htm.

Snyder, W. D.

A. Gogo, W. D. Snyder, and M. Beck, “Comparing quantum and classical correlations in a quantum eraser,” Phys. Rev. A 71, 052103 (2005).
[CrossRef]

Teich, M. C.

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: theory and experiment,” Phys. Rev. A 53, 4360-4371 (1996)
[CrossRef] [PubMed]

Tsuda, Y.

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, “Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond laser pulses,” Phys. Rev. A 66, 033816 (2002)
[CrossRef]

Usami, K.

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, “Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond laser pulses,” Phys. Rev. A 66, 033816 (2002)
[CrossRef]

Waks, E.

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

White, A. G.

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

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

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003), pp. 69-120.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003), pp. 69-120.

Am. J. Phys. (1)

D. Dehlinger and M. W. Mitchell, “Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory,” Am. J. Phys. 70, 903-910 (2002).
[CrossRef]

J. Phys. A (1)

G. M. D'Ariano, L. Maccone, and M. G. A. Paris, “Quorum of observables for universal quantum estimation,” J. Phys. A 34, 93-104 (2001).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (10)

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

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, “Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond laser pulses,” Phys. Rev. A 66, 033816 (2002)
[CrossRef]

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: theory and experiment,” Phys. Rev. A 53, 4360-4371 (1996)
[CrossRef] [PubMed]

K. Blushs and M. Auzinsh, “Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation,” Phys. Rev. A 69, 063806 (2004).
[CrossRef]

K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (2000).
[CrossRef]

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

A. Gogo, W. D. Snyder, and M. Beck, “Comparing quantum and classical correlations in a quantum eraser,” Phys. Rev. A 71, 052103 (2005).
[CrossRef]

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122-5133(1994).
[CrossRef] [PubMed]

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409-2418 (1985).
[CrossRef] [PubMed]

G. Brida, M. Chekhova, M. Genovese, and L. Krivitsky, “Generation of different bell state within spontaneous parametric down-conversion phase-matching bandwidth,” Phys. Rev. A 76, 053807 (2007)
[CrossRef]

Other (3)

A. V. Smith, SNLO nonlinear optics software, Sandia National Laboratories, http://www.sandia.gov/imrl/X1118/xxtal.htm.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003), pp. 69-120.

M.G. A.Paris and J.Rehacek, eds., “Quantum state estimation,” Lect. Notes Phys. 649, 1-4 (2004).

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Figures (4)

Fig. 1
Fig. 1

Experimental apparatus for generating and analyzing entangled states.

Fig. 2
Fig. 2

Entangled photon generation and propagation inside the crystals. For clarity, only signal photon trajectories are drawn. o and e indicate ordinary and extraordinary rays, respectively; L c is the length of both crystals.

Fig. 3
Fig. 3

Tomographic reconstruction of the generated state for three different crystals. In the fourth plot we show the calculated visibility (curve) as well as the values (full circles) obtained from the reconstructed density matrix for the three crystal pairs: 0.77 visibility for 0.5 mm crystals, 0.50 for 1 mm , and 0.09 for 3 mm .

Fig. 4
Fig. 4

Tomographic reconstruction with a delay compensation crystal (see text). (a) Crystal angle set for maximum compensation, visibility 0.66. (b) Crystal angle at 90 ° with respect to (a), visibility 0.17.

Equations (9)

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| Ψ = d ω p d ω f ( ω ) A ( ω p ) × 1 2 [ e - i ϕ H - i ω p τ H | H , ω s | H , ω p - ω i + e - i ϕ V - i ω p τ V | V , ω s | V , ω p - ω i ] ,
τ V = 1 2 L c cos ( ϕ 1 ) V SPDC ( o ) + L c cos ( ϕ 2 ) V SPDC ( e ) ,
τ H = 1 2 L c V pump ( o ) + 1 2 L c V pump ( e ) + 1 2 L c cos ( ϕ 3 ) V SPDC ( o ) ,
d ω p A ( ω p ) e - i ω p t = A 0 e i δ ( t ) ,
ρ = d ω p d ω i ω p ω | s ω | Ψ Ψ | ω s | ω p - ω i .
ρ H H , H H = 1 2 d ω | f ( ω ) | 2 d ω p | A ( ω p ) | 2 = 1 2 ϵ A 0 2 Δ T 2 π ,
ρ H H , V V = 1 2 d ω | f ( ω ) | 2 d ω p | A ( ω p ) | 2 e - i ( ϕ H - ϕ V ) e i ω p ( τ H τ V ) = 1 2 ϵ e 1 ϕ d ω p | A ( ω p ) | 2 e i ω p ( τ H τ V ) = ρ V V , H H * ,
d ω p | A ( ω p ) | 2 e i ω p ( τ H τ V ) = A 0 2 Δ T 2 π ( 1 Δ T Δ T d t e i δ ( t ) + δ [ t ( τ H τ V ) ] ) = A 0 2 Δ T 2 π e - Δ τ τ c ,
H H H V V H V V H H H V V H V V [ 1 2 0 0 1 2 e - Δ τ / τ c 0 0 0 0 0 0 0 0 1 2 e - Δ τ / τ c 0 0 1 2 ] .

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