Abstract

Group delay of electromagnetic pulses through multilayer dielectric mirrors (MDM) combined with gravitational wave (GW) is investigated. Unlike in traditional quantum tunneling, the group delay of a transmitted wave packet irradiated by a GW increases linearly with MDM length. This peculiar tunneling effect can be attributed to electromagnetic wave leakage in a time-dependent photonic bandgap caused by the GW. In particular, we find that the group delay of the tunneling photons is sensitive to GW. Our study provides insight into the nature of the quantum tunnelling as well as a novel process by which to detect the GW.

© 2013 OSA

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  1. E. U. Condon and P. M. Morse, “Quantum mechanics of collision processes I. Scattering of particles in a definite force field,” Rev. Mod. Phys.3, 43–88 (1931).
    [CrossRef]
  2. L. A. MacColl, “Note on the transmission and reflection of wave packets by potential barriers,” Phys. Rev.40, 621–626 (1932).
    [CrossRef]
  3. T. E. Hartman, “Tunneling of a wave packet,” J. Appl. Phys.33, 3427–3433 (1962).
    [CrossRef]
  4. R. Landauer and T. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys.66, 217–228 (1994).
    [CrossRef]
  5. H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox,” Phys. Rep.436, 1–69 (2006).
    [CrossRef]
  6. Ph. Balcou and L. Dutriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett.78, 851–854 (1997).
    [CrossRef]
  7. D. J. Papoular, P. Clade, S. V. Polyakov, C. F. McCormick, A. L. Migdall, and P. D. Lett, “Measuring optical tunneling times using a Hong-Ou-Mandel interferometer,” Optics Express16, 16005–16012 (2008).
    [CrossRef] [PubMed]
  8. D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
    [CrossRef] [PubMed]
  9. A. I. Baz’, “Lifetime of intermediate states,” Sov.J. Nucl. Phys.4, 182–188(1967).
  10. V. Rybachenko, “Time penetration of a particle through a potential barrier,” Sov.J. Nucl. Phys.5, 635–639 (1967).
  11. M. Büttiker and R. Landauer, “Traversal time for tunneling,” Phys. Rev. Lett.49, 1739–1742 (1982).
    [CrossRef]
  12. H. G. Winful, “Delay time and the Hartman effect in quantum tunneling,” Phys. Rev. Lett.91, 260401 (2003).
    [CrossRef]
  13. P. Krekora, Q. Su, and R. Grobe, “Effects of relativity on the time-resolved tunneling of electron wave packets,” Phys. Rev. A63, 032107 (2001).
    [CrossRef]
  14. J. T. Liu, F. H. Su, H. Wang, and X. H. Deng, “Optical field modulation on the group delay of chiral tunneling in graphene,” New J. Phys.14, 013012 (2012).
    [CrossRef]
  15. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “R. Y. Measurement of the single-photon tunneling time,” Phys. Rev. Lett.71, 708–711 (1993).
    [CrossRef] [PubMed]
  16. Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of Optical Pulses through Photonic Band Gaps,” Phys. Rev. Lett.73, 2308–2311 (1994).
    [CrossRef] [PubMed]
  17. L. G. Wang, N. H. Liu, Q. Lin, and S. Y. Zhu, “Superluminal propagation of light pulses: A result of interference,” Phys. Rev. E68, 066606 (2003).
    [CrossRef]
  18. J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett.84, 1431–1434 (2000).
    [CrossRef] [PubMed]
  19. C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett.91, 133903 (2003).
    [CrossRef] [PubMed]
  20. A. Einstein, “Die Grundlage der allgemeinen Relativitätstheorie,” Ann. Phys.49, 769–822 (1916).
    [CrossRef]
  21. J. M. Weisberg and J. H. Taylor, “The Relativistic Binary Pulsar B1913+16,” inRadio Pulsars, ASP Conf. Ser. 302, M. Bailes, D. J. Nice, and S. E. Thorsett, ed. (Chania, 2003) pp. 93–98.
  22. P. Aufmuth and K. Danzmann, “Gravitational wave detectors,” New J. Phys.7, 202 (2005).
    [CrossRef]
  23. G. M. Harry, for the LIGO scientific collaboration , “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav.27, 084006 (2010).
    [CrossRef]
  24. B. Willke, for the GEO collaboration, “The GEO-HF project,” Class. Quantum Grav.23, S207–S214 (2006).
    [CrossRef]
  25. The Virgo collaboration, “Status of the Virgo project,” Class. Quantum Grav.28, 114002 (2011).
  26. J. Weber, “Detection and generation of gravitational waves,” Phys. Rev.117, 306–313 (1960).
    [CrossRef]
  27. R. Weiss, “Electromagnetically Coupled Broadband Gravitational Antenna,” Quarterly Progress Report, Research Laboratory of Electronics, MIT10554 (1972).
  28. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas and Propag.14, 302–307 (1966).
    [CrossRef]
  29. J. R. Zurita-Sánchez, J. H. Abundis-Patiño, and P. Halevi, “Pulse propagation through a slab with time-periodic dielectric function ε(t),” Opt Express20, 5586–5600 (2012).
    [CrossRef]
  30. J. G. Bellido and D. G. Figueroa, “Stochastic background of gravitational waves from hybrid preheating,” Phys. Rev. Lett.98, 061302 (2007).
    [CrossRef]
  31. A. Rotti and T. Souradeep, “New window into stochastic gravitational wave background,” Phys. Rev. Lett.109, 221301 (2012).
    [CrossRef]
  32. V. Mandic, E. Thrane, S. Giampanis, and T. Regimbau, “Parameter estimation in searches for the stochastic gravitational-wave background,” Phys. Rev. Lett.109, 171102 (2012).
    [CrossRef] [PubMed]
  33. S. Y. Zhong, X. Wu, S. Q. Liu, and X. F. Deng, “Global symplectic structure-preserving integrators for spinning compact binaries,” Phys. Rev. D82, 124040 (2010).
    [CrossRef]
  34. S. W. Hawking and W. Israel, General Relativity, an Einstein Centenary Survey (Cambridge, 1976).

2012

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
[CrossRef] [PubMed]

J. T. Liu, F. H. Su, H. Wang, and X. H. Deng, “Optical field modulation on the group delay of chiral tunneling in graphene,” New J. Phys.14, 013012 (2012).
[CrossRef]

J. R. Zurita-Sánchez, J. H. Abundis-Patiño, and P. Halevi, “Pulse propagation through a slab with time-periodic dielectric function ε(t),” Opt Express20, 5586–5600 (2012).
[CrossRef]

A. Rotti and T. Souradeep, “New window into stochastic gravitational wave background,” Phys. Rev. Lett.109, 221301 (2012).
[CrossRef]

V. Mandic, E. Thrane, S. Giampanis, and T. Regimbau, “Parameter estimation in searches for the stochastic gravitational-wave background,” Phys. Rev. Lett.109, 171102 (2012).
[CrossRef] [PubMed]

2011

The Virgo collaboration, “Status of the Virgo project,” Class. Quantum Grav.28, 114002 (2011).

2010

G. M. Harry, for the LIGO scientific collaboration , “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav.27, 084006 (2010).
[CrossRef]

S. Y. Zhong, X. Wu, S. Q. Liu, and X. F. Deng, “Global symplectic structure-preserving integrators for spinning compact binaries,” Phys. Rev. D82, 124040 (2010).
[CrossRef]

2008

D. J. Papoular, P. Clade, S. V. Polyakov, C. F. McCormick, A. L. Migdall, and P. D. Lett, “Measuring optical tunneling times using a Hong-Ou-Mandel interferometer,” Optics Express16, 16005–16012 (2008).
[CrossRef] [PubMed]

2007

J. G. Bellido and D. G. Figueroa, “Stochastic background of gravitational waves from hybrid preheating,” Phys. Rev. Lett.98, 061302 (2007).
[CrossRef]

2006

B. Willke, for the GEO collaboration, “The GEO-HF project,” Class. Quantum Grav.23, S207–S214 (2006).
[CrossRef]

H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox,” Phys. Rep.436, 1–69 (2006).
[CrossRef]

2005

P. Aufmuth and K. Danzmann, “Gravitational wave detectors,” New J. Phys.7, 202 (2005).
[CrossRef]

2003

C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett.91, 133903 (2003).
[CrossRef] [PubMed]

H. G. Winful, “Delay time and the Hartman effect in quantum tunneling,” Phys. Rev. Lett.91, 260401 (2003).
[CrossRef]

L. G. Wang, N. H. Liu, Q. Lin, and S. Y. Zhu, “Superluminal propagation of light pulses: A result of interference,” Phys. Rev. E68, 066606 (2003).
[CrossRef]

2001

P. Krekora, Q. Su, and R. Grobe, “Effects of relativity on the time-resolved tunneling of electron wave packets,” Phys. Rev. A63, 032107 (2001).
[CrossRef]

2000

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett.84, 1431–1434 (2000).
[CrossRef] [PubMed]

1997

Ph. Balcou and L. Dutriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett.78, 851–854 (1997).
[CrossRef]

1994

R. Landauer and T. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys.66, 217–228 (1994).
[CrossRef]

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of Optical Pulses through Photonic Band Gaps,” Phys. Rev. Lett.73, 2308–2311 (1994).
[CrossRef] [PubMed]

1993

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “R. Y. Measurement of the single-photon tunneling time,” Phys. Rev. Lett.71, 708–711 (1993).
[CrossRef] [PubMed]

1982

M. Büttiker and R. Landauer, “Traversal time for tunneling,” Phys. Rev. Lett.49, 1739–1742 (1982).
[CrossRef]

1972

R. Weiss, “Electromagnetically Coupled Broadband Gravitational Antenna,” Quarterly Progress Report, Research Laboratory of Electronics, MIT10554 (1972).

1967

A. I. Baz’, “Lifetime of intermediate states,” Sov.J. Nucl. Phys.4, 182–188(1967).

V. Rybachenko, “Time penetration of a particle through a potential barrier,” Sov.J. Nucl. Phys.5, 635–639 (1967).

1966

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas and Propag.14, 302–307 (1966).
[CrossRef]

1962

T. E. Hartman, “Tunneling of a wave packet,” J. Appl. Phys.33, 3427–3433 (1962).
[CrossRef]

1960

J. Weber, “Detection and generation of gravitational waves,” Phys. Rev.117, 306–313 (1960).
[CrossRef]

1932

L. A. MacColl, “Note on the transmission and reflection of wave packets by potential barriers,” Phys. Rev.40, 621–626 (1932).
[CrossRef]

1931

E. U. Condon and P. M. Morse, “Quantum mechanics of collision processes I. Scattering of particles in a definite force field,” Rev. Mod. Phys.3, 43–88 (1931).
[CrossRef]

1916

A. Einstein, “Die Grundlage der allgemeinen Relativitätstheorie,” Ann. Phys.49, 769–822 (1916).
[CrossRef]

Abundis-Patiño, J. H.

J. R. Zurita-Sánchez, J. H. Abundis-Patiño, and P. Halevi, “Pulse propagation through a slab with time-periodic dielectric function ε(t),” Opt Express20, 5586–5600 (2012).
[CrossRef]

Aufmuth, P.

P. Aufmuth and K. Danzmann, “Gravitational wave detectors,” New J. Phys.7, 202 (2005).
[CrossRef]

Balcou, Ph.

Ph. Balcou and L. Dutriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett.78, 851–854 (1997).
[CrossRef]

Baz’, A. I.

A. I. Baz’, “Lifetime of intermediate states,” Sov.J. Nucl. Phys.4, 182–188(1967).

Bellido, J. G.

J. G. Bellido and D. G. Figueroa, “Stochastic background of gravitational waves from hybrid preheating,” Phys. Rev. Lett.98, 061302 (2007).
[CrossRef]

Bruner, B. D.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
[CrossRef] [PubMed]

Büttiker, M.

M. Büttiker and R. Landauer, “Traversal time for tunneling,” Phys. Rev. Lett.49, 1739–1742 (1982).
[CrossRef]

Carey, J. J.

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett.84, 1431–1434 (2000).
[CrossRef] [PubMed]

Chiao, R. Y.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “R. Y. Measurement of the single-photon tunneling time,” Phys. Rev. Lett.71, 708–711 (1993).
[CrossRef] [PubMed]

Clade, P.

D. J. Papoular, P. Clade, S. V. Polyakov, C. F. McCormick, A. L. Migdall, and P. D. Lett, “Measuring optical tunneling times using a Hong-Ou-Mandel interferometer,” Optics Express16, 16005–16012 (2008).
[CrossRef] [PubMed]

Condon, E. U.

E. U. Condon and P. M. Morse, “Quantum mechanics of collision processes I. Scattering of particles in a definite force field,” Rev. Mod. Phys.3, 43–88 (1931).
[CrossRef]

Dagan, M.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
[CrossRef] [PubMed]

Danzmann, K.

P. Aufmuth and K. Danzmann, “Gravitational wave detectors,” New J. Phys.7, 202 (2005).
[CrossRef]

Deng, X. F.

S. Y. Zhong, X. Wu, S. Q. Liu, and X. F. Deng, “Global symplectic structure-preserving integrators for spinning compact binaries,” Phys. Rev. D82, 124040 (2010).
[CrossRef]

Deng, X. H.

J. T. Liu, F. H. Su, H. Wang, and X. H. Deng, “Optical field modulation on the group delay of chiral tunneling in graphene,” New J. Phys.14, 013012 (2012).
[CrossRef]

Dudovich, Nirit

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
[CrossRef] [PubMed]

Dutriaux, L.

Ph. Balcou and L. Dutriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett.78, 851–854 (1997).
[CrossRef]

Einstein, A.

A. Einstein, “Die Grundlage der allgemeinen Relativitätstheorie,” Ann. Phys.49, 769–822 (1916).
[CrossRef]

Figueroa, D. G.

J. G. Bellido and D. G. Figueroa, “Stochastic background of gravitational waves from hybrid preheating,” Phys. Rev. Lett.98, 061302 (2007).
[CrossRef]

Giampanis, S.

V. Mandic, E. Thrane, S. Giampanis, and T. Regimbau, “Parameter estimation in searches for the stochastic gravitational-wave background,” Phys. Rev. Lett.109, 171102 (2012).
[CrossRef] [PubMed]

Grobe, R.

P. Krekora, Q. Su, and R. Grobe, “Effects of relativity on the time-resolved tunneling of electron wave packets,” Phys. Rev. A63, 032107 (2001).
[CrossRef]

Halevi, P.

J. R. Zurita-Sánchez, J. H. Abundis-Patiño, and P. Halevi, “Pulse propagation through a slab with time-periodic dielectric function ε(t),” Opt Express20, 5586–5600 (2012).
[CrossRef]

Harry, G. M.

G. M. Harry, for the LIGO scientific collaboration , “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav.27, 084006 (2010).
[CrossRef]

Hartman, T. E.

T. E. Hartman, “Tunneling of a wave packet,” J. Appl. Phys.33, 3427–3433 (1962).
[CrossRef]

Hawking, S. W.

S. W. Hawking and W. Israel, General Relativity, an Einstein Centenary Survey (Cambridge, 1976).

Israel, W.

S. W. Hawking and W. Israel, General Relativity, an Einstein Centenary Survey (Cambridge, 1976).

Ivanov, M. Yu.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
[CrossRef] [PubMed]

Jaroszynski, D. A.

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett.84, 1431–1434 (2000).
[CrossRef] [PubMed]

Krausz, F.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of Optical Pulses through Photonic Band Gaps,” Phys. Rev. Lett.73, 2308–2311 (1994).
[CrossRef] [PubMed]

Krekora, P.

P. Krekora, Q. Su, and R. Grobe, “Effects of relativity on the time-resolved tunneling of electron wave packets,” Phys. Rev. A63, 032107 (2001).
[CrossRef]

Kwiat, P. G.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “R. Y. Measurement of the single-photon tunneling time,” Phys. Rev. Lett.71, 708–711 (1993).
[CrossRef] [PubMed]

Landauer, R.

R. Landauer and T. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys.66, 217–228 (1994).
[CrossRef]

M. Büttiker and R. Landauer, “Traversal time for tunneling,” Phys. Rev. Lett.49, 1739–1742 (1982).
[CrossRef]

Lett, P. D.

D. J. Papoular, P. Clade, S. V. Polyakov, C. F. McCormick, A. L. Migdall, and P. D. Lett, “Measuring optical tunneling times using a Hong-Ou-Mandel interferometer,” Optics Express16, 16005–16012 (2008).
[CrossRef] [PubMed]

Li, C. F.

C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett.91, 133903 (2003).
[CrossRef] [PubMed]

Lin, Q.

L. G. Wang, N. H. Liu, Q. Lin, and S. Y. Zhu, “Superluminal propagation of light pulses: A result of interference,” Phys. Rev. E68, 066606 (2003).
[CrossRef]

Liu, J. T.

J. T. Liu, F. H. Su, H. Wang, and X. H. Deng, “Optical field modulation on the group delay of chiral tunneling in graphene,” New J. Phys.14, 013012 (2012).
[CrossRef]

Liu, N. H.

L. G. Wang, N. H. Liu, Q. Lin, and S. Y. Zhu, “Superluminal propagation of light pulses: A result of interference,” Phys. Rev. E68, 066606 (2003).
[CrossRef]

Liu, S. Q.

S. Y. Zhong, X. Wu, S. Q. Liu, and X. F. Deng, “Global symplectic structure-preserving integrators for spinning compact binaries,” Phys. Rev. D82, 124040 (2010).
[CrossRef]

MacColl, L. A.

L. A. MacColl, “Note on the transmission and reflection of wave packets by potential barriers,” Phys. Rev.40, 621–626 (1932).
[CrossRef]

Mairesse, Y.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
[CrossRef] [PubMed]

Mandic, V.

V. Mandic, E. Thrane, S. Giampanis, and T. Regimbau, “Parameter estimation in searches for the stochastic gravitational-wave background,” Phys. Rev. Lett.109, 171102 (2012).
[CrossRef] [PubMed]

Martin, T.

R. Landauer and T. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys.66, 217–228 (1994).
[CrossRef]

McCormick, C. F.

D. J. Papoular, P. Clade, S. V. Polyakov, C. F. McCormick, A. L. Migdall, and P. D. Lett, “Measuring optical tunneling times using a Hong-Ou-Mandel interferometer,” Optics Express16, 16005–16012 (2008).
[CrossRef] [PubMed]

Migdall, A. L.

D. J. Papoular, P. Clade, S. V. Polyakov, C. F. McCormick, A. L. Migdall, and P. D. Lett, “Measuring optical tunneling times using a Hong-Ou-Mandel interferometer,” Optics Express16, 16005–16012 (2008).
[CrossRef] [PubMed]

Morse, P. M.

E. U. Condon and P. M. Morse, “Quantum mechanics of collision processes I. Scattering of particles in a definite force field,” Rev. Mod. Phys.3, 43–88 (1931).
[CrossRef]

Papoular, D. J.

D. J. Papoular, P. Clade, S. V. Polyakov, C. F. McCormick, A. L. Migdall, and P. D. Lett, “Measuring optical tunneling times using a Hong-Ou-Mandel interferometer,” Optics Express16, 16005–16012 (2008).
[CrossRef] [PubMed]

Patchkovskii, S.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
[CrossRef] [PubMed]

Polyakov, S. V.

D. J. Papoular, P. Clade, S. V. Polyakov, C. F. McCormick, A. L. Migdall, and P. D. Lett, “Measuring optical tunneling times using a Hong-Ou-Mandel interferometer,” Optics Express16, 16005–16012 (2008).
[CrossRef] [PubMed]

Regimbau, T.

V. Mandic, E. Thrane, S. Giampanis, and T. Regimbau, “Parameter estimation in searches for the stochastic gravitational-wave background,” Phys. Rev. Lett.109, 171102 (2012).
[CrossRef] [PubMed]

Rotti, A.

A. Rotti and T. Souradeep, “New window into stochastic gravitational wave background,” Phys. Rev. Lett.109, 221301 (2012).
[CrossRef]

Rybachenko, V.

V. Rybachenko, “Time penetration of a particle through a potential barrier,” Sov.J. Nucl. Phys.5, 635–639 (1967).

Shafir, D.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
[CrossRef] [PubMed]

Smirnova, O.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
[CrossRef] [PubMed]

Soifer, H.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and Nirit Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature485, 343–346 (2012).
[CrossRef] [PubMed]

Souradeep, T.

A. Rotti and T. Souradeep, “New window into stochastic gravitational wave background,” Phys. Rev. Lett.109, 221301 (2012).
[CrossRef]

Spielmann, Ch.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of Optical Pulses through Photonic Band Gaps,” Phys. Rev. Lett.73, 2308–2311 (1994).
[CrossRef] [PubMed]

Steinberg, A. M.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “R. Y. Measurement of the single-photon tunneling time,” Phys. Rev. Lett.71, 708–711 (1993).
[CrossRef] [PubMed]

Stingl, A.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of Optical Pulses through Photonic Band Gaps,” Phys. Rev. Lett.73, 2308–2311 (1994).
[CrossRef] [PubMed]

Su, F. H.

J. T. Liu, F. H. Su, H. Wang, and X. H. Deng, “Optical field modulation on the group delay of chiral tunneling in graphene,” New J. Phys.14, 013012 (2012).
[CrossRef]

Su, Q.

P. Krekora, Q. Su, and R. Grobe, “Effects of relativity on the time-resolved tunneling of electron wave packets,” Phys. Rev. A63, 032107 (2001).
[CrossRef]

Szipöcs, R.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of Optical Pulses through Photonic Band Gaps,” Phys. Rev. Lett.73, 2308–2311 (1994).
[CrossRef] [PubMed]

Taylor, J. H.

J. M. Weisberg and J. H. Taylor, “The Relativistic Binary Pulsar B1913+16,” inRadio Pulsars, ASP Conf. Ser. 302, M. Bailes, D. J. Nice, and S. E. Thorsett, ed. (Chania, 2003) pp. 93–98.

Thrane, E.

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J. M. Weisberg and J. H. Taylor, “The Relativistic Binary Pulsar B1913+16,” inRadio Pulsars, ASP Conf. Ser. 302, M. Bailes, D. J. Nice, and S. E. Thorsett, ed. (Chania, 2003) pp. 93–98.

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Figures (2)

Fig. 1
Fig. 1

(a) Schematic diagram of the tunneling process in an MDM structure. (b) Group delay for the reflected wave packet and (c) that for the transmitted wave packet as a function of the number of MDM periods. Incident (black lines), tunneled (red lines) and reflected (green lines) pulses with GW amplitude AGW = 1 × 10−4 for the following number of MDM periods: (d) nMDM = 3, (e) nMDM = 19, and (f) nMDM = 30. The inset shows the normalized tunneled pulse overlaid with the incident pulse.

Fig. 2
Fig. 2

(a) Group delay of the transmitted wave packet as a function of the number of MDM periods for different GW frequencies with AGW = 1 × 10−4. (b) Group delay of the transmitted wave packet as a function of the number of MDM periods for different vacuum layer thicknesses with AGW = 1 × 10−4, ωGW = 0.1ω0, and τ0 = 2000T0. The inset shows the relative group delay as a function of the number of MDM periods.

Equations (2)

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z R / D = h 22 / 2 = A G W cos ( ω G W t ) / 2 ,
{ E x n + 1 ( m ) = E x n ( m ) Δ t ε Δ z ϒ G W [ H y n + 1 / 2 ( m + 1 / 2 ) H y n + 1 / 2 ( m 1 / 2 ) ] , H y n + 1 / 2 ( m + 1 / 2 ) = H y n 1 / 2 ( m + 1 / 2 ) Δ t μ Δ z ϒ G W [ E x n + 1 ( m + 1 ) E x n ( m ) ] ,

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