Abstract

In this paper, we propose a scheme to produce a multiplexed entanglement frequency comb in a type II phase-matching nondegenerate optical parametric amplifier (NOPA) operating below threshold. The entanglement of the signal and idler frequency combs in the wide frequency range, which is limited by the phase-matching bandwidth of the NOPA, is investigated by the inseparability criterion. Furthermore, N Einstein–Podolsky–Rosen pairs can be created from the two combs without any reduction in the correlations by using frequency-dependent beam splitters.

© 2013 Optical Society of America

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  1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [CrossRef]
  2. F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
    [CrossRef]
  3. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
    [CrossRef]
  4. B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
    [CrossRef]
  5. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).
  6. R. J. Senior, G. N. Milford, J. Janousek, A. E. Dunlop, K. Wagner, H.-A. Bachor, T. C. Ralph, E. H. Huntington, and C. C. Harb, “Observation of a comb of optical squeezing over many gigahertz of bandwidth,” Opt. Express 15, 5310–5317 (2007).
    [CrossRef]
  7. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  8. P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
    [CrossRef]
  9. L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
    [CrossRef]
  10. S. A. Diddams, L.-S. Ma, J. Ye, and J. L. Hall, “Broadband optical frequency comb generation with a phase-modulated parametric oscillator,” Opt. Lett 24, 1747–1749 (1999).
    [CrossRef]
  11. G. J. de Valcárcel, G. Patera, N. Treps, and C. Fabre, “Multimode squeezing of frequency combs,” Phys. Rev. A 74, 061801 (2006).
    [CrossRef]
  12. Y. B. Yu, S. N. Zhu, X. Q. Yu, P. Xu, J. F. Wang, Z. D. Xie, and H. Y. Leng, “Continuous-variable pair-entanglement frequency comb generated from an optical superlattice by enhanced Raman scattering,” Phys. Rev. A 77, 032317 (2008).
    [CrossRef]
  13. A. E. Dunlop and E. H. Huntington, “Generation of a frequency comb of squeezing in an optical parametric oscillator,” Phys. Rev. A 73, 013817 (2006).
    [CrossRef]
  14. D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett 102, 163601 (2009).
    [CrossRef]
  15. O. Pinel, P. Jian, R. Medeiros de Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett 108, 083601 (2012).
    [CrossRef]
  16. Y. F. Bai, P. Xu, Z. D. Xie, Y. X. Gong, and S. N. Zhu, “Mode-locked biphoton generation by concurrent quasi-phase-matching,” Phys. Rev. A 85, 053807 (2012).
    [CrossRef]
  17. M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
    [CrossRef]
  18. M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
    [CrossRef]
  19. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
    [CrossRef]
  20. J. Zhang, “Einstein-Podolsky-Rosen sideband entanglement in broadband squeezed light,” Phys. Rev. A 67, 054302 (2003).
    [CrossRef]
  21. E. H. Huntington, G. N. Milford, C. Robilliard, and T. C. Ralph, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71, 041802 (2005).
    [CrossRef]

2012 (2)

O. Pinel, P. Jian, R. Medeiros de Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett 108, 083601 (2012).
[CrossRef]

Y. F. Bai, P. Xu, Z. D. Xie, Y. X. Gong, and S. N. Zhu, “Mode-locked biphoton generation by concurrent quasi-phase-matching,” Phys. Rev. A 85, 053807 (2012).
[CrossRef]

2009 (1)

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett 102, 163601 (2009).
[CrossRef]

2008 (1)

Y. B. Yu, S. N. Zhu, X. Q. Yu, P. Xu, J. F. Wang, Z. D. Xie, and H. Y. Leng, “Continuous-variable pair-entanglement frequency comb generated from an optical superlattice by enhanced Raman scattering,” Phys. Rev. A 77, 032317 (2008).
[CrossRef]

2007 (1)

2006 (2)

G. J. de Valcárcel, G. Patera, N. Treps, and C. Fabre, “Multimode squeezing of frequency combs,” Phys. Rev. A 74, 061801 (2006).
[CrossRef]

A. E. Dunlop and E. H. Huntington, “Generation of a frequency comb of squeezing in an optical parametric oscillator,” Phys. Rev. A 73, 013817 (2006).
[CrossRef]

2005 (2)

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[CrossRef]

E. H. Huntington, G. N. Milford, C. Robilliard, and T. C. Ralph, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71, 041802 (2005).
[CrossRef]

2003 (2)

J. Zhang, “Einstein-Podolsky-Rosen sideband entanglement in broadband squeezed light,” Phys. Rev. A 67, 054302 (2003).
[CrossRef]

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[CrossRef]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

2000 (1)

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

1999 (1)

S. A. Diddams, L.-S. Ma, J. Ye, and J. L. Hall, “Broadband optical frequency comb generation with a phase-modulated parametric oscillator,” Opt. Lett 24, 1747–1749 (1999).
[CrossRef]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

1991 (1)

B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
[CrossRef]

1986 (1)

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[CrossRef]

1984 (1)

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

1981 (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[CrossRef]

Bachor, H.-A.

Bai, Y. F.

Y. F. Bai, P. Xu, Z. D. Xie, Y. X. Gong, and S. N. Zhu, “Mode-locked biphoton generation by concurrent quasi-phase-matching,” Phys. Rev. A 85, 053807 (2012).
[CrossRef]

Banaszek, K.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Brouri, R.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[CrossRef]

Carlson, D. R.

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett 102, 163601 (2009).
[CrossRef]

Caves, C. M.

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[CrossRef]

Cerf, N. J.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[CrossRef]

Chalopin, B.

O. Pinel, P. Jian, R. Medeiros de Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett 108, 083601 (2012).
[CrossRef]

Chuang, I.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Cirac, J. I.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Collett, M. J.

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

de Valcárcel, G. J.

G. J. de Valcárcel, G. Patera, N. Treps, and C. Fabre, “Multimode squeezing of frequency combs,” Phys. Rev. A 74, 061801 (2006).
[CrossRef]

Diddams, S. A.

S. A. Diddams, L.-S. Ma, J. Ye, and J. L. Hall, “Broadband optical frequency comb generation with a phase-modulated parametric oscillator,” Opt. Lett 24, 1747–1749 (1999).
[CrossRef]

Duan, L.-M.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Dunlop, A. E.

Fabre, C.

O. Pinel, P. Jian, R. Medeiros de Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett 108, 083601 (2012).
[CrossRef]

G. J. de Valcárcel, G. Patera, N. Treps, and C. Fabre, “Multimode squeezing of frequency combs,” Phys. Rev. A 74, 061801 (2006).
[CrossRef]

Feng, J.

O. Pinel, P. Jian, R. Medeiros de Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett 108, 083601 (2012).
[CrossRef]

Gardiner, C. W.

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

Giedke, G.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Gong, Y. X.

Y. F. Bai, P. Xu, Z. D. Xie, Y. X. Gong, and S. N. Zhu, “Mode-locked biphoton generation by concurrent quasi-phase-matching,” Phys. Rev. A 85, 053807 (2012).
[CrossRef]

Grangier, P.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[CrossRef]

Grosshans, F.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[CrossRef]

Hall, J. L.

S. A. Diddams, L.-S. Ma, J. Ye, and J. L. Hall, “Broadband optical frequency comb generation with a phase-modulated parametric oscillator,” Opt. Lett 24, 1747–1749 (1999).
[CrossRef]

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[CrossRef]

Harb, C. C.

Holland, M. J.

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett 102, 163601 (2009).
[CrossRef]

Huntington, E. H.

R. J. Senior, G. N. Milford, J. Janousek, A. E. Dunlop, K. Wagner, H.-A. Bachor, T. C. Ralph, E. H. Huntington, and C. C. Harb, “Observation of a comb of optical squeezing over many gigahertz of bandwidth,” Opt. Express 15, 5310–5317 (2007).
[CrossRef]

A. E. Dunlop and E. H. Huntington, “Generation of a frequency comb of squeezing in an optical parametric oscillator,” Phys. Rev. A 73, 013817 (2006).
[CrossRef]

E. H. Huntington, G. N. Milford, C. Robilliard, and T. C. Ralph, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71, 041802 (2005).
[CrossRef]

Janousek, J.

Jian, P.

O. Pinel, P. Jian, R. Medeiros de Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett 108, 083601 (2012).
[CrossRef]

Kimble, H. J.

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[CrossRef]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Leng, H. Y.

Y. B. Yu, S. N. Zhu, X. Q. Yu, P. Xu, J. F. Wang, Z. D. Xie, and H. Y. Leng, “Continuous-variable pair-entanglement frequency comb generated from an optical superlattice by enhanced Raman scattering,” Phys. Rev. A 77, 032317 (2008).
[CrossRef]

Ma, L.-S.

S. A. Diddams, L.-S. Ma, J. Ye, and J. L. Hall, “Broadband optical frequency comb generation with a phase-modulated parametric oscillator,” Opt. Lett 24, 1747–1749 (1999).
[CrossRef]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Medeiros de Araujo, R.

O. Pinel, P. Jian, R. Medeiros de Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett 108, 083601 (2012).
[CrossRef]

Meers, B. J.

B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
[CrossRef]

Meiser, D.

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett 102, 163601 (2009).
[CrossRef]

Milford, G. N.

R. J. Senior, G. N. Milford, J. Janousek, A. E. Dunlop, K. Wagner, H.-A. Bachor, T. C. Ralph, E. H. Huntington, and C. C. Harb, “Observation of a comb of optical squeezing over many gigahertz of bandwidth,” Opt. Express 15, 5310–5317 (2007).
[CrossRef]

E. H. Huntington, G. N. Milford, C. Robilliard, and T. C. Ralph, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71, 041802 (2005).
[CrossRef]

Nielsen, M.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Noh, J.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[CrossRef]

Patera, G.

G. J. de Valcárcel, G. Patera, N. Treps, and C. Fabre, “Multimode squeezing of frequency combs,” Phys. Rev. A 74, 061801 (2006).
[CrossRef]

Pinel, O.

O. Pinel, P. Jian, R. Medeiros de Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett 108, 083601 (2012).
[CrossRef]

Ralph, T. C.

R. J. Senior, G. N. Milford, J. Janousek, A. E. Dunlop, K. Wagner, H.-A. Bachor, T. C. Ralph, E. H. Huntington, and C. C. Harb, “Observation of a comb of optical squeezing over many gigahertz of bandwidth,” Opt. Express 15, 5310–5317 (2007).
[CrossRef]

E. H. Huntington, G. N. Milford, C. Robilliard, and T. C. Ralph, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71, 041802 (2005).
[CrossRef]

Raymer, M. G.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[CrossRef]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Robilliard, C.

E. H. Huntington, G. N. Milford, C. Robilliard, and T. C. Ralph, “Demonstration of the spatial separation of the entangled quantum sidebands of an optical field,” Phys. Rev. A 71, 041802 (2005).
[CrossRef]

Senior, R. J.

Strain, K. A.

B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Treps, N.

O. Pinel, P. Jian, R. Medeiros de Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett 108, 083601 (2012).
[CrossRef]

G. J. de Valcárcel, G. Patera, N. Treps, and C. Fabre, “Multimode squeezing of frequency combs,” Phys. Rev. A 74, 061801 (2006).
[CrossRef]

Van Assche, G.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[CrossRef]

Wagner, K.

Walmsley, I. A.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[CrossRef]

Wang, J. F.

Y. B. Yu, S. N. Zhu, X. Q. Yu, P. Xu, J. F. Wang, Z. D. Xie, and H. Y. Leng, “Continuous-variable pair-entanglement frequency comb generated from an optical superlattice by enhanced Raman scattering,” Phys. Rev. A 77, 032317 (2008).
[CrossRef]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Wenger, J.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[CrossRef]

Wu, H.

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[CrossRef]

Wu, L. A.

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[CrossRef]

Xie, Z. D.

Y. F. Bai, P. Xu, Z. D. Xie, Y. X. Gong, and S. N. Zhu, “Mode-locked biphoton generation by concurrent quasi-phase-matching,” Phys. Rev. A 85, 053807 (2012).
[CrossRef]

Y. B. Yu, S. N. Zhu, X. Q. Yu, P. Xu, J. F. Wang, Z. D. Xie, and H. Y. Leng, “Continuous-variable pair-entanglement frequency comb generated from an optical superlattice by enhanced Raman scattering,” Phys. Rev. A 77, 032317 (2008).
[CrossRef]

Xu, P.

Y. F. Bai, P. Xu, Z. D. Xie, Y. X. Gong, and S. N. Zhu, “Mode-locked biphoton generation by concurrent quasi-phase-matching,” Phys. Rev. A 85, 053807 (2012).
[CrossRef]

Y. B. Yu, S. N. Zhu, X. Q. Yu, P. Xu, J. F. Wang, Z. D. Xie, and H. Y. Leng, “Continuous-variable pair-entanglement frequency comb generated from an optical superlattice by enhanced Raman scattering,” Phys. Rev. A 77, 032317 (2008).
[CrossRef]

Ye, J.

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett 102, 163601 (2009).
[CrossRef]

S. A. Diddams, L.-S. Ma, J. Ye, and J. L. Hall, “Broadband optical frequency comb generation with a phase-modulated parametric oscillator,” Opt. Lett 24, 1747–1749 (1999).
[CrossRef]

Yu, X. Q.

Y. B. Yu, S. N. Zhu, X. Q. Yu, P. Xu, J. F. Wang, Z. D. Xie, and H. Y. Leng, “Continuous-variable pair-entanglement frequency comb generated from an optical superlattice by enhanced Raman scattering,” Phys. Rev. A 77, 032317 (2008).
[CrossRef]

Yu, Y. B.

Y. B. Yu, S. N. Zhu, X. Q. Yu, P. Xu, J. F. Wang, Z. D. Xie, and H. Y. Leng, “Continuous-variable pair-entanglement frequency comb generated from an optical superlattice by enhanced Raman scattering,” Phys. Rev. A 77, 032317 (2008).
[CrossRef]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Zeilinger, A.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Zhang, J.

J. Zhang, “Einstein-Podolsky-Rosen sideband entanglement in broadband squeezed light,” Phys. Rev. A 67, 054302 (2003).
[CrossRef]

Zhu, S. N.

Y. F. Bai, P. Xu, Z. D. Xie, Y. X. Gong, and S. N. Zhu, “Mode-locked biphoton generation by concurrent quasi-phase-matching,” Phys. Rev. A 85, 053807 (2012).
[CrossRef]

Y. B. Yu, S. N. Zhu, X. Q. Yu, P. Xu, J. F. Wang, Z. D. Xie, and H. Y. Leng, “Continuous-variable pair-entanglement frequency comb generated from an optical superlattice by enhanced Raman scattering,” Phys. Rev. A 77, 032317 (2008).
[CrossRef]

Zoller, P.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Nature (1)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett (1)

S. A. Diddams, L.-S. Ma, J. Ye, and J. L. Hall, “Broadband optical frequency comb generation with a phase-modulated parametric oscillator,” Opt. Lett 24, 1747–1749 (1999).
[CrossRef]

Phys. Rev. A (9)

G. J. de Valcárcel, G. Patera, N. Treps, and C. Fabre, “Multimode squeezing of frequency combs,” Phys. Rev. A 74, 061801 (2006).
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Figures (5)

Fig. 1.
Fig. 1.

Multiplexed entanglement frequency-comb generation from a NOPA. (a) Layout of quantum quadrature entanglement system. (b) Detailed project of NOPA as an optical frequency-comb generator.

Fig. 2.
Fig. 2.

Same amplitude and phase quadrature variances for the signal and idler modes, corresponding to the same comb. (a) Two sets of “up” frequency combs above the short noise level. (b) Zoom for the zeroth-order comb.

Fig. 3.
Fig. 3.

Correlation spectra of amplitude and phase quadrature variances for the two output modes (signal and idler beams), which are below shot noise level. (a) Amplitude quadrature sum V1out+2out+(ω). (b) Phase quadrature difference V1out2out(ω). (c), (d) Zooms of the zeroth-order correlation for amplitude and phase quadrature variances.

Fig. 4.
Fig. 4.

(a) Vinseparability versus analysis frequency ω. (b) Vinseparability versus pump coefficient σ at the center of one random resonance band frequency.

Fig. 5.
Fig. 5.

Schematic illustration of N EPR entanglement-pair generation by way of linear optics from the two combs using a polarization beam splitter (PBS) and 2N FDBS.

Equations (22)

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H=iχ(2)(a^0a^1a^2a^0a^1a^2).
a^˙1=k1a^1χ(2)a^0a^2+2k1b^1in(t),
a^˙2=k2a^2χ(2)a^0a^1+2k2b^2in(t).
a^1(t+τ)=χτa^2+(1kτ)a^1+2kτb^1in(t),
a^2(t+τ)=χτa^1+(1kτ)a^2+2kτb^2in(t).
δa^1(t+τ)=χτδa^2+(1kτ)δa^1+2kτδb^1in(t),
δa^2(t+τ)=χτδa^1+(1kτ)δa^2+2kτδb^2in(t).
δa^1(ω)[eiωτ(1kτ)]=χτδa^2(ω)+2kτδb^1in(ω),
δa^2(ω)[eiωτ(1kτ)]=χτδa^1(ω)+2kτδb^2in(ω).
δa^1(ω)=2kτδb^1in(ω)[eiωτ(1kτ)]2kχτ2δb^2in(ω)[eiωτ(1kτ)]2χ2τ2,
δa^2(ω)=2kτδb^2in(ω)[eiωτ(1kτ)]2kχτ2δb^1in(ω)[eiωτ(1kτ)][eiωτ(1kτ)]χ2τ2.
A^1(2)out=2ka^1(2)b^1(2)in.
δA^1out(ω)=[(k1eiωττ)(k+1eiωττ)+χ2]δb^1in(ω)2kχδb^2in(ω)(k1eiωττ)2χ2,
δA^2out(ω)=[(k1eiωττ)(k+1eiωττ)+χ2]δb^2in(ω)2kχδb^1in(ω)(k1eiωττ)2χ2.
δX^1(2)+(ω)=δA^1(2)out(ω)+δA^1(2)out(ω),
δX^1(2)(ω)=i[δA^1(2)out(ω)δA^1(2)out(ω)],
δX^1(2)in+(ω)=δb^1(2)in(ω)+δb^1(2)in(ω),
δX^1(2)in(ω)=i[δb^1(2)in(ω)δb^1(2)in(ω)],
V1out±(ω)=|k2+χ2(1eiωττ)2(k1eiωττ)2χ2|2V1in±+|2kχ(k1eiωττ)2χ2|2V2in±,
V2out±(ω)=|k2+χ2(1eiωττ)2(k1eiωττ)2χ2|2V2in±+|2kχ(k1eiωττ)2χ2|2V1in±.
V1out+2out+(ω)=|(kχ)2(1eiωττ)2(k1eiωττ)2χ2|2V1in++|(kχ)2(1eiωττ)2(k1eiωττ)2χ2|2V2in+,
V1out2out(ω)=|(kχ)2(1eiωττ)2(k1eiωττ)2χ2|2V1in+|(kχ)2(1eiωττ)2(k1eiωττ)2χ2|2V2in.

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