Abstract

With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is, electrodynamics of a polarizable medium, and numerical simulations in an elementary problem of light propagating through a slab of matter. The standard optics fails already at quite low atom densities, and the failure becomes dramatic when the average interatomic separation is reduced to around k−1, where k is the wave number of resonant light. The difference between the two solutions originates from correlations between the atoms induced by light-mediated dipole-dipole interactions.

© 2016 Optical Society of America

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References

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  1. J. D. Jackson, Classical Electrodynamics (Wiley, 1999), 3rd ed.
  2. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), 7th ed.
    [Crossref]
  3. H. Bender, C. Stehle, S. Slama, R. Kaiser, N. Piovella, C. Zimmermann, and P. W. Courteille, “Observation of cooperative Mie scattering from an ultracold atomic cloud,” Phys. Rev. A 82, 011404 (2010).
    [Crossref]
  4. S. Balik, A. L. Win, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, “Near-resonance light scattering from a high-density ultracold atomic 87Rb gas,” Phys. Rev. A 87, 053817 (2013).
    [Crossref]
  5. J. Keaveney, A. Sargsyan, U. Krohn, I. G. Hughes, D. Sarkisyan, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
    [Crossref] [PubMed]
  6. J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, “Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble,” Phys. Rev. Lett. 113, 133602 (2014).
    [Crossref] [PubMed]
  7. K. Kemp, S. J. Roof, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, “Cooperatively enhanced light transmission in cold atomic matter,” http://arxiv.org/abs/1410.2497 (2014).
  8. J. Javanainen, J. Ruostekoski, B. Vestergaard, and M. R. Francis, “One-dimensional modeling of light propagation in dense and degenerate samples,” Phys. Rev. A 59, 649–666 (1999).
    [Crossref]
  9. F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing Anderson localization of light via decay rate statistics,” Phys. Rev. E 69, 026605 (2004).
    [Crossref]
  10. S. D. Jenkins and J. Ruostekoski., “Controlled manipulation of light by cooperative response of atoms in an optical lattice,” Phys. Rev. A 86, 031602 (2012).
    [Crossref]
  11. L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New Journal of Physics 14, 055001 (2012).
    [Crossref]
  12. S. D. Jenkins and J. Ruostekoski, “Theoretical formalism for collective electromagnetic response of discrete metamaterial systems,” Phys. Rev. B 86, 085116 (2012).
    [Crossref]
  13. M. Antezza and Y. Castin, “Photonic band gap in an imperfect atomic diamond lattice: Penetration depth and effects of finite size and vacancies,” Phys. Rev. A 88, 033844 (2013).
    [Crossref]
  14. S. E. Skipetrov and I. M. Sokolov, “Absence of Anderson localization of light in a random ensemble of point scatterers,” Phys. Rev. Lett. 112, 023905 (2014).
    [Crossref] [PubMed]
  15. J. Javanainen, J. Ruostekoski, Y. Li, and S.-M. Yoo, “Shifts of a resonance line in a dense atomic sample,” Phys. Rev. Lett. 112, 113603 (2014).
    [Crossref] [PubMed]
  16. J. Ruostekoski and J. Javanainen, “Quantum field theory of cooperative atom response: Low light intensity,” Phys. Rev. A 55, 513–526 (1997).
    [Crossref]
  17. O. Morice, Y. Castin, and J. Dalibard, “Refractive index of a dilute Bose gas,” Phys. Rev. A 51, 3896–3901 (1995).
    [Crossref] [PubMed]
  18. R. Friedberg, S. Hartmann, and J. Manassah, “Frequency shifts in emission and absorption by resonant systems ot two-level atoms,” Physics Reports 7, 101–179 (1973).
    [Crossref]
  19. J. Ruostekoski and J. Javanainen, “Optical linewidth of a low density Fermi-Dirac gas,” Phys. Rev. Lett. 82, 4741–4744 (1999).
    [Crossref]
  20. R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb shift in single-photon superradiance,” Science 328, 1248–1251 (2010).
    [Crossref] [PubMed]
  21. M. O. Scully and A. A. Svidzinsky, “The Lamb shift—yesterday, today, and tomorrow,” Science 328, 1239–1241 (2010).
    [Crossref] [PubMed]
  22. T. Bienaime, R. Bachelard, N. Piovella, and R. Kaiser, “Cooperativity in light scattering by cold atoms,” Fortschr. Phys. 61, 377–392 (2013).
    [Crossref]

2014 (3)

J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, “Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble,” Phys. Rev. Lett. 113, 133602 (2014).
[Crossref] [PubMed]

S. E. Skipetrov and I. M. Sokolov, “Absence of Anderson localization of light in a random ensemble of point scatterers,” Phys. Rev. Lett. 112, 023905 (2014).
[Crossref] [PubMed]

J. Javanainen, J. Ruostekoski, Y. Li, and S.-M. Yoo, “Shifts of a resonance line in a dense atomic sample,” Phys. Rev. Lett. 112, 113603 (2014).
[Crossref] [PubMed]

2013 (3)

M. Antezza and Y. Castin, “Photonic band gap in an imperfect atomic diamond lattice: Penetration depth and effects of finite size and vacancies,” Phys. Rev. A 88, 033844 (2013).
[Crossref]

S. Balik, A. L. Win, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, “Near-resonance light scattering from a high-density ultracold atomic 87Rb gas,” Phys. Rev. A 87, 053817 (2013).
[Crossref]

T. Bienaime, R. Bachelard, N. Piovella, and R. Kaiser, “Cooperativity in light scattering by cold atoms,” Fortschr. Phys. 61, 377–392 (2013).
[Crossref]

2012 (4)

J. Keaveney, A. Sargsyan, U. Krohn, I. G. Hughes, D. Sarkisyan, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[Crossref] [PubMed]

S. D. Jenkins and J. Ruostekoski., “Controlled manipulation of light by cooperative response of atoms in an optical lattice,” Phys. Rev. A 86, 031602 (2012).
[Crossref]

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New Journal of Physics 14, 055001 (2012).
[Crossref]

S. D. Jenkins and J. Ruostekoski, “Theoretical formalism for collective electromagnetic response of discrete metamaterial systems,” Phys. Rev. B 86, 085116 (2012).
[Crossref]

2010 (3)

H. Bender, C. Stehle, S. Slama, R. Kaiser, N. Piovella, C. Zimmermann, and P. W. Courteille, “Observation of cooperative Mie scattering from an ultracold atomic cloud,” Phys. Rev. A 82, 011404 (2010).
[Crossref]

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb shift in single-photon superradiance,” Science 328, 1248–1251 (2010).
[Crossref] [PubMed]

M. O. Scully and A. A. Svidzinsky, “The Lamb shift—yesterday, today, and tomorrow,” Science 328, 1239–1241 (2010).
[Crossref] [PubMed]

2004 (1)

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing Anderson localization of light via decay rate statistics,” Phys. Rev. E 69, 026605 (2004).
[Crossref]

1999 (2)

J. Javanainen, J. Ruostekoski, B. Vestergaard, and M. R. Francis, “One-dimensional modeling of light propagation in dense and degenerate samples,” Phys. Rev. A 59, 649–666 (1999).
[Crossref]

J. Ruostekoski and J. Javanainen, “Optical linewidth of a low density Fermi-Dirac gas,” Phys. Rev. Lett. 82, 4741–4744 (1999).
[Crossref]

1997 (1)

J. Ruostekoski and J. Javanainen, “Quantum field theory of cooperative atom response: Low light intensity,” Phys. Rev. A 55, 513–526 (1997).
[Crossref]

1995 (1)

O. Morice, Y. Castin, and J. Dalibard, “Refractive index of a dilute Bose gas,” Phys. Rev. A 51, 3896–3901 (1995).
[Crossref] [PubMed]

1973 (1)

R. Friedberg, S. Hartmann, and J. Manassah, “Frequency shifts in emission and absorption by resonant systems ot two-level atoms,” Physics Reports 7, 101–179 (1973).
[Crossref]

Adams, C. S.

J. Keaveney, A. Sargsyan, U. Krohn, I. G. Hughes, D. Sarkisyan, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[Crossref] [PubMed]

Antezza, M.

M. Antezza and Y. Castin, “Photonic band gap in an imperfect atomic diamond lattice: Penetration depth and effects of finite size and vacancies,” Phys. Rev. A 88, 033844 (2013).
[Crossref]

Bachelard, R.

T. Bienaime, R. Bachelard, N. Piovella, and R. Kaiser, “Cooperativity in light scattering by cold atoms,” Fortschr. Phys. 61, 377–392 (2013).
[Crossref]

Balik, S.

S. Balik, A. L. Win, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, “Near-resonance light scattering from a high-density ultracold atomic 87Rb gas,” Phys. Rev. A 87, 053817 (2013).
[Crossref]

Bender, H.

H. Bender, C. Stehle, S. Slama, R. Kaiser, N. Piovella, C. Zimmermann, and P. W. Courteille, “Observation of cooperative Mie scattering from an ultracold atomic cloud,” Phys. Rev. A 82, 011404 (2010).
[Crossref]

Bienaime, T.

T. Bienaime, R. Bachelard, N. Piovella, and R. Kaiser, “Cooperativity in light scattering by cold atoms,” Fortschr. Phys. 61, 377–392 (2013).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), 7th ed.
[Crossref]

Bourgain, R.

J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, “Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble,” Phys. Rev. Lett. 113, 133602 (2014).
[Crossref] [PubMed]

Browaeys, A.

J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, “Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble,” Phys. Rev. Lett. 113, 133602 (2014).
[Crossref] [PubMed]

Castin, Y.

M. Antezza and Y. Castin, “Photonic band gap in an imperfect atomic diamond lattice: Penetration depth and effects of finite size and vacancies,” Phys. Rev. A 88, 033844 (2013).
[Crossref]

O. Morice, Y. Castin, and J. Dalibard, “Refractive index of a dilute Bose gas,” Phys. Rev. A 51, 3896–3901 (1995).
[Crossref] [PubMed]

Chomaz, L.

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New Journal of Physics 14, 055001 (2012).
[Crossref]

Corman, L.

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New Journal of Physics 14, 055001 (2012).
[Crossref]

Couet, S.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb shift in single-photon superradiance,” Science 328, 1248–1251 (2010).
[Crossref] [PubMed]

Courteille, P. W.

H. Bender, C. Stehle, S. Slama, R. Kaiser, N. Piovella, C. Zimmermann, and P. W. Courteille, “Observation of cooperative Mie scattering from an ultracold atomic cloud,” Phys. Rev. A 82, 011404 (2010).
[Crossref]

Dalibard, J.

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New Journal of Physics 14, 055001 (2012).
[Crossref]

O. Morice, Y. Castin, and J. Dalibard, “Refractive index of a dilute Bose gas,” Phys. Rev. A 51, 3896–3901 (1995).
[Crossref] [PubMed]

Desbuquois, R.

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New Journal of Physics 14, 055001 (2012).
[Crossref]

Francis, M. R.

J. Javanainen, J. Ruostekoski, B. Vestergaard, and M. R. Francis, “One-dimensional modeling of light propagation in dense and degenerate samples,” Phys. Rev. A 59, 649–666 (1999).
[Crossref]

Friedberg, R.

R. Friedberg, S. Hartmann, and J. Manassah, “Frequency shifts in emission and absorption by resonant systems ot two-level atoms,” Physics Reports 7, 101–179 (1973).
[Crossref]

Hartmann, S.

R. Friedberg, S. Hartmann, and J. Manassah, “Frequency shifts in emission and absorption by resonant systems ot two-level atoms,” Physics Reports 7, 101–179 (1973).
[Crossref]

Havey, M. D.

S. Balik, A. L. Win, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, “Near-resonance light scattering from a high-density ultracold atomic 87Rb gas,” Phys. Rev. A 87, 053817 (2013).
[Crossref]

Hughes, I. G.

J. Keaveney, A. Sargsyan, U. Krohn, I. G. Hughes, D. Sarkisyan, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[Crossref] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999), 3rd ed.

Javanainen, J.

J. Javanainen, J. Ruostekoski, Y. Li, and S.-M. Yoo, “Shifts of a resonance line in a dense atomic sample,” Phys. Rev. Lett. 112, 113603 (2014).
[Crossref] [PubMed]

J. Ruostekoski and J. Javanainen, “Optical linewidth of a low density Fermi-Dirac gas,” Phys. Rev. Lett. 82, 4741–4744 (1999).
[Crossref]

J. Javanainen, J. Ruostekoski, B. Vestergaard, and M. R. Francis, “One-dimensional modeling of light propagation in dense and degenerate samples,” Phys. Rev. A 59, 649–666 (1999).
[Crossref]

J. Ruostekoski and J. Javanainen, “Quantum field theory of cooperative atom response: Low light intensity,” Phys. Rev. A 55, 513–526 (1997).
[Crossref]

Jenkins, S. D.

J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, “Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble,” Phys. Rev. Lett. 113, 133602 (2014).
[Crossref] [PubMed]

S. D. Jenkins and J. Ruostekoski., “Controlled manipulation of light by cooperative response of atoms in an optical lattice,” Phys. Rev. A 86, 031602 (2012).
[Crossref]

S. D. Jenkins and J. Ruostekoski, “Theoretical formalism for collective electromagnetic response of discrete metamaterial systems,” Phys. Rev. B 86, 085116 (2012).
[Crossref]

Jennewein, S.

J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, “Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble,” Phys. Rev. Lett. 113, 133602 (2014).
[Crossref] [PubMed]

Kaiser, R.

T. Bienaime, R. Bachelard, N. Piovella, and R. Kaiser, “Cooperativity in light scattering by cold atoms,” Fortschr. Phys. 61, 377–392 (2013).
[Crossref]

H. Bender, C. Stehle, S. Slama, R. Kaiser, N. Piovella, C. Zimmermann, and P. W. Courteille, “Observation of cooperative Mie scattering from an ultracold atomic cloud,” Phys. Rev. A 82, 011404 (2010).
[Crossref]

Keaveney, J.

J. Keaveney, A. Sargsyan, U. Krohn, I. G. Hughes, D. Sarkisyan, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[Crossref] [PubMed]

Krohn, U.

J. Keaveney, A. Sargsyan, U. Krohn, I. G. Hughes, D. Sarkisyan, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[Crossref] [PubMed]

Kupriyanov, D. V.

S. Balik, A. L. Win, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, “Near-resonance light scattering from a high-density ultracold atomic 87Rb gas,” Phys. Rev. A 87, 053817 (2013).
[Crossref]

Li, Y.

J. Javanainen, J. Ruostekoski, Y. Li, and S.-M. Yoo, “Shifts of a resonance line in a dense atomic sample,” Phys. Rev. Lett. 112, 113603 (2014).
[Crossref] [PubMed]

Manassah, J.

R. Friedberg, S. Hartmann, and J. Manassah, “Frequency shifts in emission and absorption by resonant systems ot two-level atoms,” Physics Reports 7, 101–179 (1973).
[Crossref]

Morice, O.

O. Morice, Y. Castin, and J. Dalibard, “Refractive index of a dilute Bose gas,” Phys. Rev. A 51, 3896–3901 (1995).
[Crossref] [PubMed]

Orlowski, A.

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing Anderson localization of light via decay rate statistics,” Phys. Rev. E 69, 026605 (2004).
[Crossref]

Pellegrino, J.

J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, “Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble,” Phys. Rev. Lett. 113, 133602 (2014).
[Crossref] [PubMed]

Pinheiro, F. A.

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing Anderson localization of light via decay rate statistics,” Phys. Rev. E 69, 026605 (2004).
[Crossref]

Piovella, N.

T. Bienaime, R. Bachelard, N. Piovella, and R. Kaiser, “Cooperativity in light scattering by cold atoms,” Fortschr. Phys. 61, 377–392 (2013).
[Crossref]

H. Bender, C. Stehle, S. Slama, R. Kaiser, N. Piovella, C. Zimmermann, and P. W. Courteille, “Observation of cooperative Mie scattering from an ultracold atomic cloud,” Phys. Rev. A 82, 011404 (2010).
[Crossref]

Röhlsberger, R.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb shift in single-photon superradiance,” Science 328, 1248–1251 (2010).
[Crossref] [PubMed]

Rüffer, R.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb shift in single-photon superradiance,” Science 328, 1248–1251 (2010).
[Crossref] [PubMed]

Ruostekoski, J.

J. Javanainen, J. Ruostekoski, Y. Li, and S.-M. Yoo, “Shifts of a resonance line in a dense atomic sample,” Phys. Rev. Lett. 112, 113603 (2014).
[Crossref] [PubMed]

J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, “Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble,” Phys. Rev. Lett. 113, 133602 (2014).
[Crossref] [PubMed]

S. D. Jenkins and J. Ruostekoski, “Theoretical formalism for collective electromagnetic response of discrete metamaterial systems,” Phys. Rev. B 86, 085116 (2012).
[Crossref]

J. Ruostekoski and J. Javanainen, “Optical linewidth of a low density Fermi-Dirac gas,” Phys. Rev. Lett. 82, 4741–4744 (1999).
[Crossref]

J. Javanainen, J. Ruostekoski, B. Vestergaard, and M. R. Francis, “One-dimensional modeling of light propagation in dense and degenerate samples,” Phys. Rev. A 59, 649–666 (1999).
[Crossref]

J. Ruostekoski and J. Javanainen, “Quantum field theory of cooperative atom response: Low light intensity,” Phys. Rev. A 55, 513–526 (1997).
[Crossref]

Ruostekoski., J.

S. D. Jenkins and J. Ruostekoski., “Controlled manipulation of light by cooperative response of atoms in an optical lattice,” Phys. Rev. A 86, 031602 (2012).
[Crossref]

Rusek, M.

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing Anderson localization of light via decay rate statistics,” Phys. Rev. E 69, 026605 (2004).
[Crossref]

Sahoo, B.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb shift in single-photon superradiance,” Science 328, 1248–1251 (2010).
[Crossref] [PubMed]

Sargsyan, A.

J. Keaveney, A. Sargsyan, U. Krohn, I. G. Hughes, D. Sarkisyan, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[Crossref] [PubMed]

Sarkisyan, D.

J. Keaveney, A. Sargsyan, U. Krohn, I. G. Hughes, D. Sarkisyan, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[Crossref] [PubMed]

Schlage, K.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb shift in single-photon superradiance,” Science 328, 1248–1251 (2010).
[Crossref] [PubMed]

Scully, M. O.

M. O. Scully and A. A. Svidzinsky, “The Lamb shift—yesterday, today, and tomorrow,” Science 328, 1239–1241 (2010).
[Crossref] [PubMed]

Skipetrov, S. E.

S. E. Skipetrov and I. M. Sokolov, “Absence of Anderson localization of light in a random ensemble of point scatterers,” Phys. Rev. Lett. 112, 023905 (2014).
[Crossref] [PubMed]

Slama, S.

H. Bender, C. Stehle, S. Slama, R. Kaiser, N. Piovella, C. Zimmermann, and P. W. Courteille, “Observation of cooperative Mie scattering from an ultracold atomic cloud,” Phys. Rev. A 82, 011404 (2010).
[Crossref]

Sokolov, I. M.

S. E. Skipetrov and I. M. Sokolov, “Absence of Anderson localization of light in a random ensemble of point scatterers,” Phys. Rev. Lett. 112, 023905 (2014).
[Crossref] [PubMed]

S. Balik, A. L. Win, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, “Near-resonance light scattering from a high-density ultracold atomic 87Rb gas,” Phys. Rev. A 87, 053817 (2013).
[Crossref]

Sortais, Y. R. P.

J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, “Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble,” Phys. Rev. Lett. 113, 133602 (2014).
[Crossref] [PubMed]

Stehle, C.

H. Bender, C. Stehle, S. Slama, R. Kaiser, N. Piovella, C. Zimmermann, and P. W. Courteille, “Observation of cooperative Mie scattering from an ultracold atomic cloud,” Phys. Rev. A 82, 011404 (2010).
[Crossref]

Svidzinsky, A. A.

M. O. Scully and A. A. Svidzinsky, “The Lamb shift—yesterday, today, and tomorrow,” Science 328, 1239–1241 (2010).
[Crossref] [PubMed]

van Tiggelen, B. A.

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing Anderson localization of light via decay rate statistics,” Phys. Rev. E 69, 026605 (2004).
[Crossref]

Vestergaard, B.

J. Javanainen, J. Ruostekoski, B. Vestergaard, and M. R. Francis, “One-dimensional modeling of light propagation in dense and degenerate samples,” Phys. Rev. A 59, 649–666 (1999).
[Crossref]

Win, A. L.

S. Balik, A. L. Win, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, “Near-resonance light scattering from a high-density ultracold atomic 87Rb gas,” Phys. Rev. A 87, 053817 (2013).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), 7th ed.
[Crossref]

Yefsah, T.

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New Journal of Physics 14, 055001 (2012).
[Crossref]

Yoo, S.-M.

J. Javanainen, J. Ruostekoski, Y. Li, and S.-M. Yoo, “Shifts of a resonance line in a dense atomic sample,” Phys. Rev. Lett. 112, 113603 (2014).
[Crossref] [PubMed]

Zimmermann, C.

H. Bender, C. Stehle, S. Slama, R. Kaiser, N. Piovella, C. Zimmermann, and P. W. Courteille, “Observation of cooperative Mie scattering from an ultracold atomic cloud,” Phys. Rev. A 82, 011404 (2010).
[Crossref]

Fortschr. Phys. (1)

T. Bienaime, R. Bachelard, N. Piovella, and R. Kaiser, “Cooperativity in light scattering by cold atoms,” Fortschr. Phys. 61, 377–392 (2013).
[Crossref]

New Journal of Physics (1)

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New Journal of Physics 14, 055001 (2012).
[Crossref]

Phys. Rev. A (7)

M. Antezza and Y. Castin, “Photonic band gap in an imperfect atomic diamond lattice: Penetration depth and effects of finite size and vacancies,” Phys. Rev. A 88, 033844 (2013).
[Crossref]

J. Ruostekoski and J. Javanainen, “Quantum field theory of cooperative atom response: Low light intensity,” Phys. Rev. A 55, 513–526 (1997).
[Crossref]

O. Morice, Y. Castin, and J. Dalibard, “Refractive index of a dilute Bose gas,” Phys. Rev. A 51, 3896–3901 (1995).
[Crossref] [PubMed]

H. Bender, C. Stehle, S. Slama, R. Kaiser, N. Piovella, C. Zimmermann, and P. W. Courteille, “Observation of cooperative Mie scattering from an ultracold atomic cloud,” Phys. Rev. A 82, 011404 (2010).
[Crossref]

S. Balik, A. L. Win, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, “Near-resonance light scattering from a high-density ultracold atomic 87Rb gas,” Phys. Rev. A 87, 053817 (2013).
[Crossref]

J. Javanainen, J. Ruostekoski, B. Vestergaard, and M. R. Francis, “One-dimensional modeling of light propagation in dense and degenerate samples,” Phys. Rev. A 59, 649–666 (1999).
[Crossref]

S. D. Jenkins and J. Ruostekoski., “Controlled manipulation of light by cooperative response of atoms in an optical lattice,” Phys. Rev. A 86, 031602 (2012).
[Crossref]

Phys. Rev. B (1)

S. D. Jenkins and J. Ruostekoski, “Theoretical formalism for collective electromagnetic response of discrete metamaterial systems,” Phys. Rev. B 86, 085116 (2012).
[Crossref]

Phys. Rev. E (1)

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing Anderson localization of light via decay rate statistics,” Phys. Rev. E 69, 026605 (2004).
[Crossref]

Phys. Rev. Lett. (5)

J. Keaveney, A. Sargsyan, U. Krohn, I. G. Hughes, D. Sarkisyan, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[Crossref] [PubMed]

J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, “Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble,” Phys. Rev. Lett. 113, 133602 (2014).
[Crossref] [PubMed]

S. E. Skipetrov and I. M. Sokolov, “Absence of Anderson localization of light in a random ensemble of point scatterers,” Phys. Rev. Lett. 112, 023905 (2014).
[Crossref] [PubMed]

J. Javanainen, J. Ruostekoski, Y. Li, and S.-M. Yoo, “Shifts of a resonance line in a dense atomic sample,” Phys. Rev. Lett. 112, 113603 (2014).
[Crossref] [PubMed]

J. Ruostekoski and J. Javanainen, “Optical linewidth of a low density Fermi-Dirac gas,” Phys. Rev. Lett. 82, 4741–4744 (1999).
[Crossref]

Physics Reports (1)

R. Friedberg, S. Hartmann, and J. Manassah, “Frequency shifts in emission and absorption by resonant systems ot two-level atoms,” Physics Reports 7, 101–179 (1973).
[Crossref]

Science (2)

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb shift in single-photon superradiance,” Science 328, 1248–1251 (2010).
[Crossref] [PubMed]

M. O. Scully and A. A. Svidzinsky, “The Lamb shift—yesterday, today, and tomorrow,” Science 328, 1239–1241 (2010).
[Crossref] [PubMed]

Other (3)

K. Kemp, S. J. Roof, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, “Cooperatively enhanced light transmission in cold atomic matter,” http://arxiv.org/abs/1410.2497 (2014).

J. D. Jackson, Classical Electrodynamics (Wiley, 1999), 3rd ed.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), 7th ed.
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Optical thickness (depth, density) of a slab of matter as a function of light-atom detuning from both standard optics and from an essentially exact numerical simulation for stationary strongly interacting atomic dipoles. The results are for the sample density ρ = k3 and slab thickness h = k−1. The truncation error in the numerical computations due to the finite area A = 1024 k−2 of the disk-shape sample, about 5%, is irrelevant for a qualitative comparison. The conspicuous difference between the two curves demonstrates the breakdown of traditional optics.
Fig. 2
Fig. 2 Ratio of the absorption coefficient from numerical computations, ��C, and from MFT, ��M, as a function of the density of the slab with the thickness h = π/k. The positive detunings are chosen in such a way that the MFT gives ��M = 0.01 for each density, an optically thin sample. The mean free path for light scattering for independently radiating atoms would therefore be approximately 100 times the thickness of the sample for all data points. Nevertheless, there are up to factor-of-ten deviations from the MFT. The numbers of atoms, obviously integers, are chosen so that for a given density the area of the disk is as close to A = 2000k−2 as possible, whereupon the truncation errors in the absorption coefficients ��C are at most a few per cent.
Fig. 3
Fig. 3 Shift of the resonance s, scaled to the absolute value of the LL shift |ΔLL|, as a function of the sample thickness h, for two densities ρ = 0.01k3 (circles) and ρ = 0.005k3 (crosses). Also shown is the prediction (2), shifted up by |ΔLL| for easier comparison (solid line). The largest optical thickness in the raw data is D ≃ 1, so for all parameter values in this figure the sample is still fairly transparent. The truncation errors in the data points are at most on the order of one per cent.
Fig. 4
Fig. 4 Light propagation through a slab of matter: Schematic representation of the electric fields at the surfaces of a slab of thickness h and refractive index n.

Equations (8)

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𝒜 M = 6 π ρ h γ 2 k 2 Δ 2 [ 1 + 3 | Δ LL | 8 h k γ ( 1 cos 2 h k ) ] + 𝒪 ( 1 Δ 3 ) .
s = Δ LL + 3 4 | Δ LL | ( 1 sin 2 h k 2 h k ) .
E T E 0 = 2 n e i k h 2 n cos n k h i ( n 2 + 1 ) sin n k h .
α = ζ Δ + i γ , ζ = 𝒟 2 h ¯ ,
χ = n 2 1 = ζ ρ Δ Δ LL + i γ , Δ LL = ζ ρ 3 ε 0 = 2 π γ ρ k 3 ,
E ( r i ) = E 0 ( r i ) + α j i G ( r i r j ) E ( r j ) .
E ( r ) = E 0 ( r ) + α j G ( r i r j ) E ( r j ) .
E j ( r ) = i k 2 π ε 0 R 2 [ d ( r j ) e ^ z d ( r j ) e ^ z ] e i k ( z z j ) .

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