Abstract

A novel fiber-based scheme for generating quadrature entanglement between a specific pair of frequency bands is proposed. The scheme is based on use of a nonlinear fiber, a spectral pulse shaper, and an adaptive feedback loop. It is numerically predicted that at least -5 dB of the quadrature entanglement will be created by preparation of an appropriate initial phase spectrum. Optimal control of the four-wave mixing terms of the Kerr Hamiltonian is crucial for improvement of the entanglement.

© 2003 Optical Society of America

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  1. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, Phys. Rev. A 60, R773 (1999).
    [CrossRef]
  2. Z. Y. Ou, S. F. Pereira, and H. J. Kimble, Appl. Phys. B 55, 265 (1992).
    [CrossRef]
  3. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurther, and A. Zeilinger, Nature 390, 575 (1997).
    [CrossRef]
  4. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).
    [CrossRef] [PubMed]
  5. Y.-H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 86, 1370 (2001).
    [CrossRef] [PubMed]
  6. A. Mair, A. Vazirl, G. Welhs, and A. Zeilinger, Nature 412, 313 (2001).
    [CrossRef] [PubMed]
  7. Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
    [CrossRef] [PubMed]
  8. E. Schmidt, L. Knöll, and D.-G. Welsch, Opt. Commun. 194, 393 (2001).
    [CrossRef]
  9. L. J. Wang, C. K. Hong, and S. R. Friberg, J. Opt. B 3, 346 (2001).
    [CrossRef]
  10. J. E. Sharping, M. Fiorentino, and P. Kumar, Opt. Lett. 26, 367 (2001).
    [CrossRef]
  11. S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
    [CrossRef] [PubMed]
  12. A. Mecozzi and P. Kumar, Opt. Lett. 22, 1232 (1997).
    [CrossRef] [PubMed]
  13. S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
    [CrossRef]
  14. M. Takeoka, D. Fujishima, and F. Kannari, Opt. Lett. 26, 1592 (2001).
    [CrossRef]
  15. A. M. Weiner, Prog. Quantum. Electron. 19, 161 (1995).
    [CrossRef]
  16. U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, Cambridge, 1997).
  17. M. Beck, C. Dorrer, and I. A. Walmsely, Phys. Rev. Lett. 87, 253601 (2001), and references therein.
    [CrossRef]
  18. Y. Lai and S.-S. Yu, Phys. Rev. A 51, 817 (1995).
    [CrossRef] [PubMed]
  19. C. X. Yu, H. A. Haus, and E. P. Ippen, Opt. Lett. 26, 669 (2001).
    [CrossRef]
  20. M. D. Levenson and R. M. Shelby, J. Mod. Opt. 34, 775 (1987).
    [CrossRef]

2001 (9)

Y.-H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 86, 1370 (2001).
[CrossRef] [PubMed]

A. Mair, A. Vazirl, G. Welhs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

E. Schmidt, L. Knöll, and D.-G. Welsch, Opt. Commun. 194, 393 (2001).
[CrossRef]

L. J. Wang, C. K. Hong, and S. R. Friberg, J. Opt. B 3, 346 (2001).
[CrossRef]

J. E. Sharping, M. Fiorentino, and P. Kumar, Opt. Lett. 26, 367 (2001).
[CrossRef]

M. Takeoka, D. Fujishima, and F. Kannari, Opt. Lett. 26, 1592 (2001).
[CrossRef]

M. Beck, C. Dorrer, and I. A. Walmsely, Phys. Rev. Lett. 87, 253601 (2001), and references therein.
[CrossRef]

C. X. Yu, H. A. Haus, and E. P. Ippen, Opt. Lett. 26, 669 (2001).
[CrossRef]

1999 (1)

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

1998 (2)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).
[CrossRef] [PubMed]

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

1997 (2)

A. Mecozzi and P. Kumar, Opt. Lett. 22, 1232 (1997).
[CrossRef] [PubMed]

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurther, and A. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

1996 (1)

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

1995 (2)

A. M. Weiner, Prog. Quantum. Electron. 19, 161 (1995).
[CrossRef]

Y. Lai and S.-S. Yu, Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

1992 (1)

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, Appl. Phys. B 55, 265 (1992).
[CrossRef]

1987 (1)

M. D. Levenson and R. M. Shelby, J. Mod. Opt. 34, 775 (1987).
[CrossRef]

Appelbaum, I.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

Beck, M.

M. Beck, C. Dorrer, and I. A. Walmsely, Phys. Rev. Lett. 87, 253601 (2001), and references therein.
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurther, and A. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Braunstein, S. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).
[CrossRef] [PubMed]

Dorrer, C.

M. Beck, C. Dorrer, and I. A. Walmsely, Phys. Rev. Lett. 87, 253601 (2001), and references therein.
[CrossRef]

Eberhard, P. H.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

Eibl, M.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurther, and A. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Fiorentino, M.

Friberg, S. R.

L. J. Wang, C. K. Hong, and S. R. Friberg, J. Opt. B 3, 346 (2001).
[CrossRef]

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

Fuchs, C. A.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).
[CrossRef] [PubMed]

Fujishima, D.

Furusawa, A.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).
[CrossRef] [PubMed]

Haus, H. A.

Hong, C. K.

L. J. Wang, C. K. Hong, and S. R. Friberg, J. Opt. B 3, 346 (2001).
[CrossRef]

Ippen, E. P.

Kannari, F.

Kim, Y.-H.

Y.-H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 86, 1370 (2001).
[CrossRef] [PubMed]

Kimble, H. J.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).
[CrossRef] [PubMed]

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, Appl. Phys. B 55, 265 (1992).
[CrossRef]

Knöll, L.

E. Schmidt, L. Knöll, and D.-G. Welsch, Opt. Commun. 194, 393 (2001).
[CrossRef]

König, F.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Korolkova, N.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Kulik, S. P.

Y.-H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 86, 1370 (2001).
[CrossRef] [PubMed]

Kumar, P.

Kwiat, P. G.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

Lai, Y.

Y. Lai and S.-S. Yu, Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

Lam, P. K.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, Cambridge, 1997).

Leuchs, G.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Levanon, A.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

Levenson, M. D.

M. D. Levenson and R. M. Shelby, J. Mod. Opt. 34, 775 (1987).
[CrossRef]

Machida, S.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vazirl, G. Welhs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Mattle, K.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurther, and A. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Mecozzi, A.

Mukai, T.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

Ou, Z. Y.

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, Appl. Phys. B 55, 265 (1992).
[CrossRef]

Pan, J.-W.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurther, and A. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Pereira, S. F.

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, Appl. Phys. B 55, 265 (1992).
[CrossRef]

Polzik, E. S.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).
[CrossRef] [PubMed]

Schmidt, E.

E. Schmidt, L. Knöll, and D.-G. Welsch, Opt. Commun. 194, 393 (2001).
[CrossRef]

Sharping, J. E.

Shelby, R. M.

M. D. Levenson and R. M. Shelby, J. Mod. Opt. 34, 775 (1987).
[CrossRef]

Shih, Y.

Y.-H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 86, 1370 (2001).
[CrossRef] [PubMed]

Silberhorn, Ch.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Sizmann, A.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Sørensen, J. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).
[CrossRef] [PubMed]

Spälter, S.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Takeoka, M.

Vazirl, A.

A. Mair, A. Vazirl, G. Welhs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Waks, E.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

Walmsely, I. A.

M. Beck, C. Dorrer, and I. A. Walmsely, Phys. Rev. Lett. 87, 253601 (2001), and references therein.
[CrossRef]

Wang, L. J.

L. J. Wang, C. K. Hong, and S. R. Friberg, J. Opt. B 3, 346 (2001).
[CrossRef]

Weiner, A. M.

A. M. Weiner, Prog. Quantum. Electron. 19, 161 (1995).
[CrossRef]

Weinfurther, H.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurther, and A. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Weiss, O.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Welhs, G.

A. Mair, A. Vazirl, G. Welhs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Welsch, D.-G.

E. Schmidt, L. Knöll, and D.-G. Welsch, Opt. Commun. 194, 393 (2001).
[CrossRef]

Werner, M. J.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

White, A. G.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

Yu, C. X.

Yu, S.-S.

Y. Lai and S.-S. Yu, Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

Zeilinger, A.

A. Mair, A. Vazirl, G. Welhs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurther, and A. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Appl. Phys. B (1)

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, Appl. Phys. B 55, 265 (1992).
[CrossRef]

J. Mod. Opt. (1)

M. D. Levenson and R. M. Shelby, J. Mod. Opt. 34, 775 (1987).
[CrossRef]

J. Opt. B (1)

L. J. Wang, C. K. Hong, and S. R. Friberg, J. Opt. B 3, 346 (2001).
[CrossRef]

Nature (2)

A. Mair, A. Vazirl, G. Welhs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurther, and A. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Opt. Commun. (1)

E. Schmidt, L. Knöll, and D.-G. Welsch, Opt. Commun. 194, 393 (2001).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (2)

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

Y. Lai and S.-S. Yu, Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

M. Beck, C. Dorrer, and I. A. Walmsely, Phys. Rev. Lett. 87, 253601 (2001), and references therein.
[CrossRef]

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Y.-H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 86, 1370 (2001).
[CrossRef] [PubMed]

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Prog. Quantum. Electron. (1)

A. M. Weiner, Prog. Quantum. Electron. 19, 161 (1995).
[CrossRef]

Science (1)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).
[CrossRef] [PubMed]

Other (1)

U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, Cambridge, 1997).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the adaptive coherent control system for generation, detection, and optimization of intrapulse frequency entanglement: BS’s, beam splitters; M’s, mirrors; L’s, lenses; G’s, gratings; SLM, spatial light modulator.

Fig. 2
Fig. 2

Optimization of the quadrature entanglement by the simulated annealing iteration. Inset, waveform of the optimally shaped pulse. Shading shows frequency bands for aˆ1 and aˆ2.

Fig. 3
Fig. 3

Complex coefficients of (a) Hˆ1 and (b) Hˆ2 for the optimally shaped pulse and the sech pulse.

Equations (6)

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

ΔXˆ1±ΔXˆ22ΔYˆ1ΔYˆ22<1/4<ΔXˆ1ΔXˆ22ΔYˆ1±ΔYˆ22,
aˆoutt=1-Γt1/2aˆint+Γt1/2cˆt,
Δnˆ=121-Γta¯LOtΔaˆ0L,t+H.c.dt,
Hˆ=Hˆ1+Hˆ2,
Hˆ1= cnχ-dωi-dωj-dωk×2a¯z,ωka¯z,ωi+ωj-ωkΔaˆz,ωi×Δaˆz,ωj+H.c.,
Hˆ2= cnχ-dωi-dωj-dωk×2a¯*z,ωka¯z,ωi-ωj+ωkΔaˆz,ωi×Δaˆz,ωj+H.c.,

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