Abstract

The quantum radiation through the multilayer structures containing the left-handed materials is investigated based on the Green-function approach to the quantization of the phenomenological Maxwell theory. Emphasis is placed on the effect of randomness on the generation and transmission of entangled-states. It is shown that some unusual properties appear for the present systems in comparison with those of the conventional dielectric structures. The quantum relative entropy is always enhanced with the increase of random degree due to the existence of nonlocalized mode in the present systems, while the maximal entanglement can be observed only at some certain randomness for the conventional dielectric structures. In contrast to exponential decrease in the conventional systems, the entanglement degrades slowly with the increase of disorder and thickness of the sample near the nonlocalized mode after transmission through the present systems. This will benefit the quantum communication for long distances.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Nielsen and I. L. Chuang, "Quantum computation and quantum information," (Cambridge University Press, Cambridge, 2000).
  2. D. Bouwmeester, A. Ekert, and A. Zeilinger, "The physics of quantum information," (Springer, 2000).
  3. A. Ekert, "Quantum cryptography based on Bell�??s theorem," Phys. Rev. Lett. 67, 661 (1991).
    [CrossRef] [PubMed]
  4. C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wooters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993).
    [CrossRef] [PubMed]
  5. S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869 (1998).
    [CrossRef]
  6. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706 (1998).
    [CrossRef] [PubMed]
  7. T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, "Quantum cryptography with entangled photons," Phys. Rev. Lett. 84, 4729 (2000).
    [CrossRef] [PubMed]
  8. J. R. Jeffers, N. Imoto, and R. Loudon, "Quantum optics of traveling-wave attenuators and amplifiers," Phys. Rev. A 47, 3346 (1993).
    [CrossRef] [PubMed]
  9. R. Matloob, R. Loudon, M. Artoni, S. M. Barnett, and J. Jeffers, "Electromagnetic field quantization in amplifying dielectrics," Phys. Rev. A 55, 1623 (1997).
    [CrossRef]
  10. M. Artoni and R. Loudon, "Quantum theory of optical pulse propagation through an absorbing and dispersive slab," Phys. Rev. A 55, 1347 (1997).
    [CrossRef]
  11. T. Gruner and D. G. Welsch, "Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates," Phys. Rev. A 54, 1661 (1996).
    [CrossRef] [PubMed]
  12. L. Knöll, S. Scheel, E. Schmidt, D. G. Welsch, and A.V. Chizhov, "Quantum-state transformation by dispersive and absorbing four-port devices," Phys. Rev. A 59, 4716 (1999).
    [CrossRef]
  13. S. Scheel, L. Knöll, T. Opatrný, and D. G. Welsch, "Entanglement transformation at absorbing and amplifying four-port devices," Phys. Rev. A 62, 043803 (2000).
    [CrossRef]
  14. M. Khanbekyan, L. Knöll, and D. G. Welsch, "Input-output relations at dispersing and absorbing planar multilayers for the quantized electromagnetic field containing evanescent components," Phys. Rev. A 67, 063812 (2003).
    [CrossRef]
  15. V. M. Agranovich and Y. N. Gartstein, "Spatial dispersion and negative refraction of light," Phys. Usp. 49, 1029 (2006).
    [CrossRef]
  16. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  17. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
    [CrossRef] [PubMed]
  18. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  19. R. Ruppin, "Extinction properties of a sphere with negative permittivity and permeability," Solid State Commun. 116, 411 (2000).
    [CrossRef]
  20. H. T. Dung, S. Y. Buhmann, L. Knöll, D. G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
    [CrossRef]
  21. Z. M. Zhang and C. J. Fu, "Unusual photon tunneling in the presence of a layer with a negative refractive index," Appl. Phys. Lett. 80, 1097 (2002).
    [CrossRef]
  22. R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  23. I. S. Nefedov and S. A. Tretyakov, "Photonic band gap structure containing metamaterial with negative permittivity and permeability," Phys. Rev. E 66, 036611 (2002).
    [CrossRef]
  24. I. V. Shadrivov, N. A. Zharova, A. A. Zharov, and Y. S. Kivshar, "Defect modes and transmission properties of left-handed bandgap structures," Phys. Rev. E 70, 046615 (2004).
    [CrossRef]
  25. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69, 165112 (2004).
    [CrossRef]
  26. I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
    [CrossRef]
  27. J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901(2003).
    [CrossRef] [PubMed]
  28. Y. Dong and X. Zhang, "Unusual transmission properties of wave in one-dimensional random system containing left-handed-material," Phys. Lett. A 359, 542 (2006).
    [CrossRef]
  29. S. M. Barnett and S. J. D. Phoenix, "Entropy as a measure of quantum optical correlation," Phys. Rev. A 40, 2404 (1989).
    [CrossRef] [PubMed]
  30. V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, "Quantifying entanglement," Phys. Rev. Lett. 78, 2275 (1997).
    [CrossRef]
  31. V. Vedral and M. B. Plenio, "Entanglement measures and purification procedures," Phys. Rev. A 57, 1619 (1998).
    [CrossRef]

2006

V. M. Agranovich and Y. N. Gartstein, "Spatial dispersion and negative refraction of light," Phys. Usp. 49, 1029 (2006).
[CrossRef]

Y. Dong and X. Zhang, "Unusual transmission properties of wave in one-dimensional random system containing left-handed-material," Phys. Lett. A 359, 542 (2006).
[CrossRef]

2004

I. V. Shadrivov, N. A. Zharova, A. A. Zharov, and Y. S. Kivshar, "Defect modes and transmission properties of left-handed bandgap structures," Phys. Rev. E 70, 046615 (2004).
[CrossRef]

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69, 165112 (2004).
[CrossRef]

2003

I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901(2003).
[CrossRef] [PubMed]

M. Khanbekyan, L. Knöll, and D. G. Welsch, "Input-output relations at dispersing and absorbing planar multilayers for the quantized electromagnetic field containing evanescent components," Phys. Rev. A 67, 063812 (2003).
[CrossRef]

H. T. Dung, S. Y. Buhmann, L. Knöll, D. G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

2002

Z. M. Zhang and C. J. Fu, "Unusual photon tunneling in the presence of a layer with a negative refractive index," Appl. Phys. Lett. 80, 1097 (2002).
[CrossRef]

I. S. Nefedov and S. A. Tretyakov, "Photonic band gap structure containing metamaterial with negative permittivity and permeability," Phys. Rev. E 66, 036611 (2002).
[CrossRef]

2001

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

2000

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

R. Ruppin, "Extinction properties of a sphere with negative permittivity and permeability," Solid State Commun. 116, 411 (2000).
[CrossRef]

S. Scheel, L. Knöll, T. Opatrný, and D. G. Welsch, "Entanglement transformation at absorbing and amplifying four-port devices," Phys. Rev. A 62, 043803 (2000).
[CrossRef]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, "Quantum cryptography with entangled photons," Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

1999

L. Knöll, S. Scheel, E. Schmidt, D. G. Welsch, and A.V. Chizhov, "Quantum-state transformation by dispersive and absorbing four-port devices," Phys. Rev. A 59, 4716 (1999).
[CrossRef]

1998

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869 (1998).
[CrossRef]

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

V. Vedral and M. B. Plenio, "Entanglement measures and purification procedures," Phys. Rev. A 57, 1619 (1998).
[CrossRef]

1997

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, "Quantifying entanglement," Phys. Rev. Lett. 78, 2275 (1997).
[CrossRef]

R. Matloob, R. Loudon, M. Artoni, S. M. Barnett, and J. Jeffers, "Electromagnetic field quantization in amplifying dielectrics," Phys. Rev. A 55, 1623 (1997).
[CrossRef]

M. Artoni and R. Loudon, "Quantum theory of optical pulse propagation through an absorbing and dispersive slab," Phys. Rev. A 55, 1347 (1997).
[CrossRef]

1996

T. Gruner and D. G. Welsch, "Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates," Phys. Rev. A 54, 1661 (1996).
[CrossRef] [PubMed]

1993

J. R. Jeffers, N. Imoto, and R. Loudon, "Quantum optics of traveling-wave attenuators and amplifiers," Phys. Rev. A 47, 3346 (1993).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wooters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

1991

A. Ekert, "Quantum cryptography based on Bell�??s theorem," Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

1989

S. M. Barnett and S. J. D. Phoenix, "Entropy as a measure of quantum optical correlation," Phys. Rev. A 40, 2404 (1989).
[CrossRef] [PubMed]

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich and Y. N. Gartstein, "Spatial dispersion and negative refraction of light," Phys. Usp. 49, 1029 (2006).
[CrossRef]

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Artoni, M.

R. Matloob, R. Loudon, M. Artoni, S. M. Barnett, and J. Jeffers, "Electromagnetic field quantization in amplifying dielectrics," Phys. Rev. A 55, 1623 (1997).
[CrossRef]

M. Artoni and R. Loudon, "Quantum theory of optical pulse propagation through an absorbing and dispersive slab," Phys. Rev. A 55, 1347 (1997).
[CrossRef]

Barnett, S. M.

R. Matloob, R. Loudon, M. Artoni, S. M. Barnett, and J. Jeffers, "Electromagnetic field quantization in amplifying dielectrics," Phys. Rev. A 55, 1623 (1997).
[CrossRef]

S. M. Barnett and S. J. D. Phoenix, "Entropy as a measure of quantum optical correlation," Phys. Rev. A 40, 2404 (1989).
[CrossRef] [PubMed]

Baughman, R. H.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wooters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wooters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Braunstein, S. L.

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869 (1998).
[CrossRef]

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

Buhmann, S. Y.

H. T. Dung, S. Y. Buhmann, L. Knöll, D. G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

Chan, C. T.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901(2003).
[CrossRef] [PubMed]

Chizhov, A.V.

L. Knöll, S. Scheel, E. Schmidt, D. G. Welsch, and A.V. Chizhov, "Quantum-state transformation by dispersive and absorbing four-port devices," Phys. Rev. A 59, 4716 (1999).
[CrossRef]

Crepeau, C.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wooters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Dong, Y.

Y. Dong and X. Zhang, "Unusual transmission properties of wave in one-dimensional random system containing left-handed-material," Phys. Lett. A 359, 542 (2006).
[CrossRef]

Dung, H. T.

H. T. Dung, S. Y. Buhmann, L. Knöll, D. G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

Ekert, A.

A. Ekert, "Quantum cryptography based on Bell�??s theorem," Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

Fu, C. J.

Z. M. Zhang and C. J. Fu, "Unusual photon tunneling in the presence of a layer with a negative refractive index," Appl. Phys. Lett. 80, 1097 (2002).
[CrossRef]

Fuchs, C. A.

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

Furusawa, A.

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

Gartstein, Y. N.

V. M. Agranovich and Y. N. Gartstein, "Spatial dispersion and negative refraction of light," Phys. Usp. 49, 1029 (2006).
[CrossRef]

Gruner, T.

T. Gruner and D. G. Welsch, "Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates," Phys. Rev. A 54, 1661 (1996).
[CrossRef] [PubMed]

Heyman, E.

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Imoto, N.

J. R. Jeffers, N. Imoto, and R. Loudon, "Quantum optics of traveling-wave attenuators and amplifiers," Phys. Rev. A 47, 3346 (1993).
[CrossRef] [PubMed]

Jeffers, J.

R. Matloob, R. Loudon, M. Artoni, S. M. Barnett, and J. Jeffers, "Electromagnetic field quantization in amplifying dielectrics," Phys. Rev. A 55, 1623 (1997).
[CrossRef]

Jeffers, J. R.

J. R. Jeffers, N. Imoto, and R. Loudon, "Quantum optics of traveling-wave attenuators and amplifiers," Phys. Rev. A 47, 3346 (1993).
[CrossRef] [PubMed]

Jennewein, T.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, "Quantum cryptography with entangled photons," Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Josza, R.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wooters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Kastel, J.

H. T. Dung, S. Y. Buhmann, L. Knöll, D. G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

Khanbekyan, M.

M. Khanbekyan, L. Knöll, and D. G. Welsch, "Input-output relations at dispersing and absorbing planar multilayers for the quantized electromagnetic field containing evanescent components," Phys. Rev. A 67, 063812 (2003).
[CrossRef]

Kimble, H. J.

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869 (1998).
[CrossRef]

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

Kivshar, Y. S.

I. V. Shadrivov, N. A. Zharova, A. A. Zharov, and Y. S. Kivshar, "Defect modes and transmission properties of left-handed bandgap structures," Phys. Rev. E 70, 046615 (2004).
[CrossRef]

Kivshar, Yu. S.

I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Knight, P. L.

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, "Quantifying entanglement," Phys. Rev. Lett. 78, 2275 (1997).
[CrossRef]

Knöll, L.

M. Khanbekyan, L. Knöll, and D. G. Welsch, "Input-output relations at dispersing and absorbing planar multilayers for the quantized electromagnetic field containing evanescent components," Phys. Rev. A 67, 063812 (2003).
[CrossRef]

H. T. Dung, S. Y. Buhmann, L. Knöll, D. G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

S. Scheel, L. Knöll, T. Opatrný, and D. G. Welsch, "Entanglement transformation at absorbing and amplifying four-port devices," Phys. Rev. A 62, 043803 (2000).
[CrossRef]

L. Knöll, S. Scheel, E. Schmidt, D. G. Welsch, and A.V. Chizhov, "Quantum-state transformation by dispersive and absorbing four-port devices," Phys. Rev. A 59, 4716 (1999).
[CrossRef]

Li, J.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901(2003).
[CrossRef] [PubMed]

Loudon, R.

M. Artoni and R. Loudon, "Quantum theory of optical pulse propagation through an absorbing and dispersive slab," Phys. Rev. A 55, 1347 (1997).
[CrossRef]

R. Matloob, R. Loudon, M. Artoni, S. M. Barnett, and J. Jeffers, "Electromagnetic field quantization in amplifying dielectrics," Phys. Rev. A 55, 1623 (1997).
[CrossRef]

J. R. Jeffers, N. Imoto, and R. Loudon, "Quantum optics of traveling-wave attenuators and amplifiers," Phys. Rev. A 47, 3346 (1993).
[CrossRef] [PubMed]

Matloob, R.

R. Matloob, R. Loudon, M. Artoni, S. M. Barnett, and J. Jeffers, "Electromagnetic field quantization in amplifying dielectrics," Phys. Rev. A 55, 1623 (1997).
[CrossRef]

Nefedov, I. S.

I. S. Nefedov and S. A. Tretyakov, "Photonic band gap structure containing metamaterial with negative permittivity and permeability," Phys. Rev. E 66, 036611 (2002).
[CrossRef]

Opatrný, T.

S. Scheel, L. Knöll, T. Opatrný, and D. G. Welsch, "Entanglement transformation at absorbing and amplifying four-port devices," Phys. Rev. A 62, 043803 (2000).
[CrossRef]

Pendry, J. B.

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Peres, A.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wooters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Phoenix, S. J. D.

S. M. Barnett and S. J. D. Phoenix, "Entropy as a measure of quantum optical correlation," Phys. Rev. A 40, 2404 (1989).
[CrossRef] [PubMed]

Plenio, M. B.

V. Vedral and M. B. Plenio, "Entanglement measures and purification procedures," Phys. Rev. A 57, 1619 (1998).
[CrossRef]

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, "Quantifying entanglement," Phys. Rev. Lett. 78, 2275 (1997).
[CrossRef]

Polzik, E. S.

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

Rippin, M. A.

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, "Quantifying entanglement," Phys. Rev. Lett. 78, 2275 (1997).
[CrossRef]

Ruppin, R.

R. Ruppin, "Extinction properties of a sphere with negative permittivity and permeability," Solid State Commun. 116, 411 (2000).
[CrossRef]

Scheel, S.

H. T. Dung, S. Y. Buhmann, L. Knöll, D. G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

S. Scheel, L. Knöll, T. Opatrný, and D. G. Welsch, "Entanglement transformation at absorbing and amplifying four-port devices," Phys. Rev. A 62, 043803 (2000).
[CrossRef]

L. Knöll, S. Scheel, E. Schmidt, D. G. Welsch, and A.V. Chizhov, "Quantum-state transformation by dispersive and absorbing four-port devices," Phys. Rev. A 59, 4716 (1999).
[CrossRef]

Schmidt, E.

L. Knöll, S. Scheel, E. Schmidt, D. G. Welsch, and A.V. Chizhov, "Quantum-state transformation by dispersive and absorbing four-port devices," Phys. Rev. A 59, 4716 (1999).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Shadrivov, I. V.

I. V. Shadrivov, N. A. Zharova, A. A. Zharov, and Y. S. Kivshar, "Defect modes and transmission properties of left-handed bandgap structures," Phys. Rev. E 70, 046615 (2004).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Shen, Y. R.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Sheng, P.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901(2003).
[CrossRef] [PubMed]

Simon, C.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, "Quantum cryptography with entangled photons," Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Sørensen, J. L.

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

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Tretyakov, S. A.

I. S. Nefedov and S. A. Tretyakov, "Photonic band gap structure containing metamaterial with negative permittivity and permeability," Phys. Rev. E 66, 036611 (2002).
[CrossRef]

Vedral, V.

V. Vedral and M. B. Plenio, "Entanglement measures and purification procedures," Phys. Rev. A 57, 1619 (1998).
[CrossRef]

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, "Quantifying entanglement," Phys. Rev. Lett. 78, 2275 (1997).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Weihs, G.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, "Quantum cryptography with entangled photons," Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Weinfurter, H.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, "Quantum cryptography with entangled photons," Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Welsch, D. G.

M. Khanbekyan, L. Knöll, and D. G. Welsch, "Input-output relations at dispersing and absorbing planar multilayers for the quantized electromagnetic field containing evanescent components," Phys. Rev. A 67, 063812 (2003).
[CrossRef]

H. T. Dung, S. Y. Buhmann, L. Knöll, D. G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

S. Scheel, L. Knöll, T. Opatrný, and D. G. Welsch, "Entanglement transformation at absorbing and amplifying four-port devices," Phys. Rev. A 62, 043803 (2000).
[CrossRef]

L. Knöll, S. Scheel, E. Schmidt, D. G. Welsch, and A.V. Chizhov, "Quantum-state transformation by dispersive and absorbing four-port devices," Phys. Rev. A 59, 4716 (1999).
[CrossRef]

T. Gruner and D. G. Welsch, "Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates," Phys. Rev. A 54, 1661 (1996).
[CrossRef] [PubMed]

Wooters, W. K.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wooters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Zakhidov, A. A.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Zeilinger, A.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, "Quantum cryptography with entangled photons," Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Zhang, X.

Y. Dong and X. Zhang, "Unusual transmission properties of wave in one-dimensional random system containing left-handed-material," Phys. Lett. A 359, 542 (2006).
[CrossRef]

Zhang, Z. M.

Z. M. Zhang and C. J. Fu, "Unusual photon tunneling in the presence of a layer with a negative refractive index," Appl. Phys. Lett. 80, 1097 (2002).
[CrossRef]

Zharov, A. A.

I. V. Shadrivov, N. A. Zharova, A. A. Zharov, and Y. S. Kivshar, "Defect modes and transmission properties of left-handed bandgap structures," Phys. Rev. E 70, 046615 (2004).
[CrossRef]

Zharova, N. A.

I. V. Shadrivov, N. A. Zharova, A. A. Zharov, and Y. S. Kivshar, "Defect modes and transmission properties of left-handed bandgap structures," Phys. Rev. E 70, 046615 (2004).
[CrossRef]

Zhou, L.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901(2003).
[CrossRef] [PubMed]

Ziolkowski, R. W.

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Appl. Phys. Lett.

Z. M. Zhang and C. J. Fu, "Unusual photon tunneling in the presence of a layer with a negative refractive index," Appl. Phys. Lett. 80, 1097 (2002).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Phys. Lett. A

Y. Dong and X. Zhang, "Unusual transmission properties of wave in one-dimensional random system containing left-handed-material," Phys. Lett. A 359, 542 (2006).
[CrossRef]

Phys. Rev. A

S. M. Barnett and S. J. D. Phoenix, "Entropy as a measure of quantum optical correlation," Phys. Rev. A 40, 2404 (1989).
[CrossRef] [PubMed]

V. Vedral and M. B. Plenio, "Entanglement measures and purification procedures," Phys. Rev. A 57, 1619 (1998).
[CrossRef]

H. T. Dung, S. Y. Buhmann, L. Knöll, D. G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

J. R. Jeffers, N. Imoto, and R. Loudon, "Quantum optics of traveling-wave attenuators and amplifiers," Phys. Rev. A 47, 3346 (1993).
[CrossRef] [PubMed]

R. Matloob, R. Loudon, M. Artoni, S. M. Barnett, and J. Jeffers, "Electromagnetic field quantization in amplifying dielectrics," Phys. Rev. A 55, 1623 (1997).
[CrossRef]

M. Artoni and R. Loudon, "Quantum theory of optical pulse propagation through an absorbing and dispersive slab," Phys. Rev. A 55, 1347 (1997).
[CrossRef]

T. Gruner and D. G. Welsch, "Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates," Phys. Rev. A 54, 1661 (1996).
[CrossRef] [PubMed]

L. Knöll, S. Scheel, E. Schmidt, D. G. Welsch, and A.V. Chizhov, "Quantum-state transformation by dispersive and absorbing four-port devices," Phys. Rev. A 59, 4716 (1999).
[CrossRef]

S. Scheel, L. Knöll, T. Opatrný, and D. G. Welsch, "Entanglement transformation at absorbing and amplifying four-port devices," Phys. Rev. A 62, 043803 (2000).
[CrossRef]

M. Khanbekyan, L. Knöll, and D. G. Welsch, "Input-output relations at dispersing and absorbing planar multilayers for the quantized electromagnetic field containing evanescent components," Phys. Rev. A 67, 063812 (2003).
[CrossRef]

Phys. Rev. B

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Phys. Rev. E

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

I. S. Nefedov and S. A. Tretyakov, "Photonic band gap structure containing metamaterial with negative permittivity and permeability," Phys. Rev. E 66, 036611 (2002).
[CrossRef]

I. V. Shadrivov, N. A. Zharova, A. A. Zharov, and Y. S. Kivshar, "Defect modes and transmission properties of left-handed bandgap structures," Phys. Rev. E 70, 046615 (2004).
[CrossRef]

Phys. Rev. Lett.

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, "Quantifying entanglement," Phys. Rev. Lett. 78, 2275 (1997).
[CrossRef]

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901(2003).
[CrossRef] [PubMed]

A. Ekert, "Quantum cryptography based on Bell�??s theorem," Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wooters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869 (1998).
[CrossRef]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, "Quantum cryptography with entangled photons," Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Phys. Usp.

V. M. Agranovich and Y. N. Gartstein, "Spatial dispersion and negative refraction of light," Phys. Usp. 49, 1029 (2006).
[CrossRef]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

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

Solid State Commun.

R. Ruppin, "Extinction properties of a sphere with negative permittivity and permeability," Solid State Commun. 116, 411 (2000).
[CrossRef]

Sov. Phys. Usp.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other

M. A. Nielsen and I. L. Chuang, "Quantum computation and quantum information," (Cambridge University Press, Cambridge, 2000).

D. Bouwmeester, A. Ekert, and A. Zeilinger, "The physics of quantum information," (Springer, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Scheme of the multilayer configuration with different frequency-dependent permittivity (ε(ω)) and permeability (µ(ω)). The arrows together with the amplitude operators indicate incoming and outgoing fields.

Fig. 2.
Fig. 2.

The transmission coefficients (a) and the total correlations (b) through the multilayer structure containing the LHMs with N=22 as a function of the reduced frequency with different random strengths. Solid line, dashed line and dotted line correspond to the case withδ=0.0,0.2,1.0, respectively.

Fig. 3.
Fig. 3.

The transmission coefficients (a) and the total correlations (b) through the multilayer structure consisting of the air and the pure dielectric material with ε=3.4 and N=22 as a function of the frequency with different random strengths. Solid line, dashed line and dotted line correspond to the case withδ=0.0,0.2,1.0, respectively.

Fig. 4.
Fig. 4.

The entanglement measure E(ρ(F) out) as a function of the random strength for structure I (a) and structure II (b) at different frequencies which are marked in the figures. The other parameters are identical to those in Figs. 2 and 3.

Fig. 5.
Fig. 5.

Comparison of entanglement degradation of entangled Bell-type state as a function of the random strength for two kinds of structure. The parameters are identical to those in Fig. 4.

Fig. 6.
Fig. 6.

Comparison of entanglement degradation of entangled Bell-type state as a function of the number of layer with δ=1.0. The other parameters are identical to those in Fig. 4.

Equations (35)

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

ε ( ω ) = 1 ω p 2 ω ( ω + i γ ) ,
μ ( ω ) = 1 F ω 2 ω 2 ω 0 2 + i ω Γ ,
x ( κ ( x , ω ) x A ̂ ( x , ω ) ) ω 2 c 2 ε ( x , ω ) A ̂ ( x , ω ) = μ 0 j ̂ N ( x , ω ) ,
j ̂ N ( x , ω ) = ω ε 0 π A ε I ( ω ) f ̂ e ( x , ω ) x π μ 0 A κ I ( ω ) f ̂ m ( x , ω ) .
A ̂ ( x , ω ) = μ 0 dx G ( x , x , ω ) j ̂ N ( x , ω ) + H . c . ,
[ x κ ( x , ω ) x + ω 2 c 2 ε ( x , ω ) ] G ( x , x , ω ) = δ ( x x ) .
G ( x , x , ω ) = μ ( ω ) 2 i ω c n ( ω ) exp [ i ω c n ( ω ) x x ] ,
A ̂ ( x ) = 0 d ω A ̂ ( x , ω ) + H . c .
= 0 d ω ζ ( ω ) 4 π ω ε 0 c Α μ ( ω ) n ( ω ) × [ e i β ( ω ) ω x c a ̂ + ( x , ω ) + e i β ( ω ) ω x c a ̂ ( x , ω ) ] + H . c . ,
a ̂ × ( x , ω ) = i 2 γ ( ω ) ω c e γ ( ω ) ω x c ± x d x in ( ω ) ω x c ε I ( ω ) f ̂ e ( ± x , ω ) in ( ω ) κ I ( ω ) f ̂ m ( ± x , ω ) ε I ( ω ) κ I ( ω ) n ( ω ) 2
ζ ( ω ) = ε I ( ω ) κ I ( ω ) n ( ω ) 2 2 γ ( ω ) .
x a ̂ ± ( x , ω ) = γ ( ω ) ω c a ̂ ( x , ω ) + F ̂ ( x , ω ) ,
F ̂ ( x , ω ) = i 2 γ ( ω ) ω c e i β ( ω ) ω x c ε I ( ω ) f ̂ e ( x , ω ) in ( ω ) κ I ( ω ) f ̂ m ( x , ω ) ε I ( ω ) κ I ( ω ) n ( ω ) 2 .
A ̂ ( x ) = 0 d ω ζ j ( ω ) 4 π ω ε 0 c Α μ j ( ω ) n j ( ω ) [ e i β j ( ω ) ω x c a ̂ j + ( x , ω ) + e i β j ( ω ) ω x c a ̂ j ( x , ω ) ] + H . c . ,
a ̂ j ± ( x , ω ) = a ̂ j ± ( x , ω ) e γ j ( ω ) ω ( x x ) c + x x dy F ̂ j ± ( y , ω ) e γ j ( ω ) ω ( x y ) c ,
F ̂ j ± ( x , ω ) = ± i 2 γ j ( ω ) ω c e i β j ( ω ) ω x / c ε j I ( ω ) f ̂ e ( x , ω ) in j ( ω ) κ j I ( ω ) f ̂ m ( x , ω ) ε j I ( ω ) κ j I ( ω ) n j ( ω ) 2 .
( a ̂ 1 ( x 1 , ω ) a ̂ N + ( x N 1 , ω ) ) = T ( N 2 ) ( ω ) ( a ̂ 1 + ( x 1 , ω ) a ̂ N ( x N 1 , ω ) ) + A ( N 2 ) ( ω ) ( g ̂ + ( N 2 ) ( ω ) g ̂ ( N 2 ) ( ω ) ) .
b ̂ ( ω ) = T ( ω ) a ̂ ( ω ) + A ( ω ) g ̂ ( ω ) ,
g ̂ ± ( 1 ) ( ω ) = [ 2 c ± ( l 2 , ω ) ] 1 2 [ g ̂ ( ω ) ± g ̂ + ( ω ) ] ,
g ̂ ± ( ω ) = i ω c e in 2 ( ω ) ω l 2 ( 2 c ) x 3 x 1 dx e in 2 ( ω ) ω x c ε 2 I ( ω ) f ̂ e ( x , ω ) in 2 ( ω ) κ 2 I ( ω ) f ̂ m ( x , ω ) ε 2 I ( ω ) κ 2 I ( ω ) n 2 ( ω ) 2 ,
c ± ( l 2 , ω ) = e γ 2 ( ω ) ω l 2 c γ 2 ( ω ) sinh [ γ 2 ( ω ) ω l 2 c ] ± ε 2 I + κ 2 I n 2 2 ε 2 I κ 2 I n 2 2 e γ 2 ( ω ) ω l 2 c β 2 ( ω ) sin [ β 2 ( ω ) ω l 2 c ] .
β ̂ ( ω ) = Λ ( ω ) α ̂ ( ω )
β ̂ ( ω ) = U ̂ ( ω ) α ̂ ( ω ) U ̂ ( ω ) ,
U ̂ = exp [ i 0 d ω [ α ̂ ( ω ) ] T Φ ( ω ) α ̂ ( ω ) ]
ρ ̂ out ( F ) = Tr ( D ) { U ̂ ρ ̂ in U ̂ + } = Tr ( D ) { ρ ̂ in [ Λ + ( ω ) α ̂ ( ω ) , Λ T ( ω ) α ̂ ( ω ) ] } ,
I c = S 1 + S 2 S 12 ,
S i = Tr [ ρ ̂ out ( F ) log 2 ( ρ ̂ out ( F ) ) ] ,
S 12 = Tr [ ρ ̂ out ( F ) log 2 ( ρ ̂ out ( F ) ) ] .
E ( ρ ̂ out ( F ) ) = min σ ̂ S T r [ ρ ̂ out ( F ) ( log 2 ρ ̂ out ( F ) log 2 σ ̂ ) ] ,
| Ψ in = | 1 , 0
ρ ̂ out ( F ) = v 00 00 + T 21 2 01 01 + T 11 * T 21 01 10 + T 21 * T 11 10 01 + T 11 2 10 10 ,
v = 1 T 11 2 T 21 2 ,
| Ψ ± = 1 2 ( | 01 ± | 10 ) ,
ρ ̂ out ( F ) = u | 00 00 | + 1 2 ( T 21 ( 1 ) 2 | 10 10 | + T 21 ( 2 ) 2 | 01 01 | ± T 21 ( 1 ) T 21 ( 2 ) * | 10 01 ± T 21 ( 1 ) * T 21 ( 2 ) 10 10 | )
u = 1 2 ( 2 T 21 ( 1 ) 2 T 21 ( 2 ) 2 ) ,

Metrics