Abstract

Energy and lifetime of collective optical excitations in regular arrays of atoms and molecules are significantly influenced by dipole-dipole interaction. While the dynamics of closely positioned atoms can be approximated well by the Dicke superradiance model, the situation of finite regular configurations is hard to access analytically. Most treatments use an exciton based description limited to the lowest excitation manifold. We present a general approach studying the complete decay cascade of a finite regular array of atoms from the fully inverted to the ground state. We explicitly calculate all energy shifts and decay rates for two generic cases of a three-atom linear chain and an equilateral triangle. In numerical calculations we show that despite fairly weak dipole-dipole interactions, collective vacuum coupling allows for superradiant emission as well as subradiant states in larger arrays through multi-particle interference. This induces extra dephasing and modified decay as important limitations for Ramsey experiments in lattice atomic clock setups as well as for the gain and frequency stability of superradiant lasers.

© 2012 OSA

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  1. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev.93, 99–110 (1954). URL http://link.aps.org/doi/10.1103/PhysRev.93.99 .
    [CrossRef]
  2. J. MacGillivray and M. Feld, “Theory of superradiance in an extended, optically thick medium,” Rhys. Rv. A14(3), 1169–1189 (1976).
  3. M. Gross and S. Haroche, “Superradiance: An essay on the theory of collective spontaneous emission,” Phys. Rep.93(5), 301–396 (1982). URL http://www.sciencedirect.com/science/article/pii/0370157382901028 .
    [CrossRef]
  4. N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke Superradiance in optically pumped HFgGas,” Phys. Rev. Lett.30, 309–312 (1973). URL http://link.aps.org/doi/10.1103/PhysRevLett.30.309 .
    [CrossRef]
  5. S. Inouye, A. Chikkatur, D. Stamper-Kurn, J. Stenger, D. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science285(5427), 571–574 (1999).
    [CrossRef] [PubMed]
  6. M. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. Lett.83(25), 5202–5205 (1999).
    [CrossRef]
  7. R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A4(1), 302–313 (1971).
    [CrossRef]
  8. N. E. Rehler and J. H. Eberly, “Superradiance,” Phys. Rev. A3, 1735–1751 (1971). URL http://link.aps.org/doi/10.1103/PhysRevA.3.1735 .
    [CrossRef]
  9. S. Davydov, Theory of Molecular Excitons (Plenum PressNew York, 1971).
  10. V. Agranovich, Excitations in Organic Solids (Oxford University Press, UK, 2009).
  11. H. Zoubi and H. Ritsch, “Lifetime and emission characteristics of collective electronic excitations in two-dimensional optical lattices,” Phys. Rev. A83(6), 063831 (2011).
    [CrossRef]
  12. H. Zoubi and H. Ritsch, “Metastability and directional emission characteristics of excitons in 1D optical lattices,” Europhys. Lett.90, 23001 (2010).
    [CrossRef]
  13. I. Carusotto, M. Antezza, F. Bariani, S. De Liberato, and C. Ciuti, “Optical properties of atomic Mott insulators: from slow light to dynamical Casimir effects,” Phys. Rev. A77(6), 063621 (2008).
    [CrossRef]
  14. M. Takamoto, F. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature435(7040), 321–324 (2005).
    [CrossRef] [PubMed]
  15. L. Casperson, “Spectral narrowing in double-pass superradiant lasers,” Optics Communications8(1), 85–87 (1973).
    [CrossRef]
  16. J. Bohnet, Z. Chen, J. Weiner, D. Meiser, M. Holland, and J. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature484(7392), 78–81 (2012).
    [CrossRef] [PubMed]
  17. K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A82(3), 033810 (2010).
    [CrossRef]
  18. Z. Ficek and R. Tanaś, “Entangled states and collective nonclassical effects in two-atom systems,” Phys. Rep.372(5), 369–443 (2002).
    [CrossRef]
  19. R. Lehmberg, “Radiation from an N-atom system. I. General formalism,” Phys. Rev. A2(3), 883–888 (1970).
    [CrossRef]
  20. J. Guo and J. Cooper, “Cooling and resonance fluorescence of two atoms in a one-dimensional optical molasses,” Phys. Rev. A51(4), 3128–3135 (1995).
    [CrossRef] [PubMed]
  21. Z. Ficek, R. Tanaś, and S. Kielich, “Quantum beats and superradiant effects in the spontaneous emission from two nonidentical atoms,” Physica A146(3), 452–482 (1987).
    [CrossRef]
  22. H. Zoubi, “Collective light emission of a finite size atomic chain,” EPL100(24002) (2012).
    [CrossRef]
  23. M. Takamoto and H. Katori, “Spectroscopy of the 1S0-3P0 Clock Transition of 87Sr in an optical lattice,” Phys. Rev. Lett.91(22), 223001 (2003).
    [CrossRef] [PubMed]
  24. I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Physics1(1), 23–30 (2005).
    [CrossRef]
  25. G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
    [CrossRef]
  26. P. Horak, K. Gheri, and H. Ritsch, “Quantum dynamics of a single-atom cascade laser,” Phys. Rev. A51(4), 3257–3266 (1995).
    [CrossRef] [PubMed]
  27. G. Lin and S. Yelin, “Superradiance in spin-j particles: effects of multiple levels,” Phys. Rev. A85(3), 033831 (2012).
    [CrossRef]

2012

J. Bohnet, Z. Chen, J. Weiner, D. Meiser, M. Holland, and J. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature484(7392), 78–81 (2012).
[CrossRef] [PubMed]

H. Zoubi, “Collective light emission of a finite size atomic chain,” EPL100(24002) (2012).
[CrossRef]

G. Lin and S. Yelin, “Superradiance in spin-j particles: effects of multiple levels,” Phys. Rev. A85(3), 033831 (2012).
[CrossRef]

2011

H. Zoubi and H. Ritsch, “Lifetime and emission characteristics of collective electronic excitations in two-dimensional optical lattices,” Phys. Rev. A83(6), 063831 (2011).
[CrossRef]

2010

H. Zoubi and H. Ritsch, “Metastability and directional emission characteristics of excitons in 1D optical lattices,” Europhys. Lett.90, 23001 (2010).
[CrossRef]

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A82(3), 033810 (2010).
[CrossRef]

2008

I. Carusotto, M. Antezza, F. Bariani, S. De Liberato, and C. Ciuti, “Optical properties of atomic Mott insulators: from slow light to dynamical Casimir effects,” Phys. Rev. A77(6), 063621 (2008).
[CrossRef]

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

2005

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Physics1(1), 23–30 (2005).
[CrossRef]

M. Takamoto, F. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature435(7040), 321–324 (2005).
[CrossRef] [PubMed]

2003

M. Takamoto and H. Katori, “Spectroscopy of the 1S0-3P0 Clock Transition of 87Sr in an optical lattice,” Phys. Rev. Lett.91(22), 223001 (2003).
[CrossRef] [PubMed]

2002

Z. Ficek and R. Tanaś, “Entangled states and collective nonclassical effects in two-atom systems,” Phys. Rep.372(5), 369–443 (2002).
[CrossRef]

1999

S. Inouye, A. Chikkatur, D. Stamper-Kurn, J. Stenger, D. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science285(5427), 571–574 (1999).
[CrossRef] [PubMed]

M. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. Lett.83(25), 5202–5205 (1999).
[CrossRef]

1995

J. Guo and J. Cooper, “Cooling and resonance fluorescence of two atoms in a one-dimensional optical molasses,” Phys. Rev. A51(4), 3128–3135 (1995).
[CrossRef] [PubMed]

P. Horak, K. Gheri, and H. Ritsch, “Quantum dynamics of a single-atom cascade laser,” Phys. Rev. A51(4), 3257–3266 (1995).
[CrossRef] [PubMed]

1987

Z. Ficek, R. Tanaś, and S. Kielich, “Quantum beats and superradiant effects in the spontaneous emission from two nonidentical atoms,” Physica A146(3), 452–482 (1987).
[CrossRef]

1982

M. Gross and S. Haroche, “Superradiance: An essay on the theory of collective spontaneous emission,” Phys. Rep.93(5), 301–396 (1982). URL http://www.sciencedirect.com/science/article/pii/0370157382901028 .
[CrossRef]

1976

J. MacGillivray and M. Feld, “Theory of superradiance in an extended, optically thick medium,” Rhys. Rv. A14(3), 1169–1189 (1976).

1973

N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke Superradiance in optically pumped HFgGas,” Phys. Rev. Lett.30, 309–312 (1973). URL http://link.aps.org/doi/10.1103/PhysRevLett.30.309 .
[CrossRef]

L. Casperson, “Spectral narrowing in double-pass superradiant lasers,” Optics Communications8(1), 85–87 (1973).
[CrossRef]

1971

R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A4(1), 302–313 (1971).
[CrossRef]

N. E. Rehler and J. H. Eberly, “Superradiance,” Phys. Rev. A3, 1735–1751 (1971). URL http://link.aps.org/doi/10.1103/PhysRevA.3.1735 .
[CrossRef]

1970

R. Lehmberg, “Radiation from an N-atom system. I. General formalism,” Phys. Rev. A2(3), 883–888 (1970).
[CrossRef]

1954

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev.93, 99–110 (1954). URL http://link.aps.org/doi/10.1103/PhysRev.93.99 .
[CrossRef]

Agranovich, V.

V. Agranovich, Excitations in Organic Solids (Oxford University Press, UK, 2009).

Antezza, M.

I. Carusotto, M. Antezza, F. Bariani, S. De Liberato, and C. Ciuti, “Optical properties of atomic Mott insulators: from slow light to dynamical Casimir effects,” Phys. Rev. A77(6), 063621 (2008).
[CrossRef]

Bariani, F.

I. Carusotto, M. Antezza, F. Bariani, S. De Liberato, and C. Ciuti, “Optical properties of atomic Mott insulators: from slow light to dynamical Casimir effects,” Phys. Rev. A77(6), 063621 (2008).
[CrossRef]

Blatt, S.

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

Bloch, I.

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Physics1(1), 23–30 (2005).
[CrossRef]

Bohnet, J.

J. Bohnet, Z. Chen, J. Weiner, D. Meiser, M. Holland, and J. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature484(7392), 78–81 (2012).
[CrossRef] [PubMed]

Bonifacio, R.

R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A4(1), 302–313 (1971).
[CrossRef]

Boyd, M.

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

Campbell, G.

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

Carusotto, I.

I. Carusotto, M. Antezza, F. Bariani, S. De Liberato, and C. Ciuti, “Optical properties of atomic Mott insulators: from slow light to dynamical Casimir effects,” Phys. Rev. A77(6), 063621 (2008).
[CrossRef]

Casperson, L.

L. Casperson, “Spectral narrowing in double-pass superradiant lasers,” Optics Communications8(1), 85–87 (1973).
[CrossRef]

Chen, Z.

J. Bohnet, Z. Chen, J. Weiner, D. Meiser, M. Holland, and J. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature484(7392), 78–81 (2012).
[CrossRef] [PubMed]

Chikkatur, A.

S. Inouye, A. Chikkatur, D. Stamper-Kurn, J. Stenger, D. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science285(5427), 571–574 (1999).
[CrossRef] [PubMed]

Ciuti, C.

I. Carusotto, M. Antezza, F. Bariani, S. De Liberato, and C. Ciuti, “Optical properties of atomic Mott insulators: from slow light to dynamical Casimir effects,” Phys. Rev. A77(6), 063621 (2008).
[CrossRef]

Cooper, J.

J. Guo and J. Cooper, “Cooling and resonance fluorescence of two atoms in a one-dimensional optical molasses,” Phys. Rev. A51(4), 3128–3135 (1995).
[CrossRef] [PubMed]

Davydov, S.

S. Davydov, Theory of Molecular Excitons (Plenum PressNew York, 1971).

De Liberato, S.

I. Carusotto, M. Antezza, F. Bariani, S. De Liberato, and C. Ciuti, “Optical properties of atomic Mott insulators: from slow light to dynamical Casimir effects,” Phys. Rev. A77(6), 063621 (2008).
[CrossRef]

de Miranda, M.

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

Dicke, R. H.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev.93, 99–110 (1954). URL http://link.aps.org/doi/10.1103/PhysRev.93.99 .
[CrossRef]

Diddams, S.

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

Eberly, J. H.

N. E. Rehler and J. H. Eberly, “Superradiance,” Phys. Rev. A3, 1735–1751 (1971). URL http://link.aps.org/doi/10.1103/PhysRevA.3.1735 .
[CrossRef]

Feld, M.

J. MacGillivray and M. Feld, “Theory of superradiance in an extended, optically thick medium,” Rhys. Rv. A14(3), 1169–1189 (1976).

Feld, M. S.

N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke Superradiance in optically pumped HFgGas,” Phys. Rev. Lett.30, 309–312 (1973). URL http://link.aps.org/doi/10.1103/PhysRevLett.30.309 .
[CrossRef]

Ficek, Z.

Z. Ficek and R. Tanaś, “Entangled states and collective nonclassical effects in two-atom systems,” Phys. Rep.372(5), 369–443 (2002).
[CrossRef]

Z. Ficek, R. Tanaś, and S. Kielich, “Quantum beats and superradiant effects in the spontaneous emission from two nonidentical atoms,” Physica A146(3), 452–482 (1987).
[CrossRef]

Gheri, K.

P. Horak, K. Gheri, and H. Ritsch, “Quantum dynamics of a single-atom cascade laser,” Phys. Rev. A51(4), 3257–3266 (1995).
[CrossRef] [PubMed]

Gross, M.

M. Gross and S. Haroche, “Superradiance: An essay on the theory of collective spontaneous emission,” Phys. Rep.93(5), 301–396 (1982). URL http://www.sciencedirect.com/science/article/pii/0370157382901028 .
[CrossRef]

Guo, J.

J. Guo and J. Cooper, “Cooling and resonance fluorescence of two atoms in a one-dimensional optical molasses,” Phys. Rev. A51(4), 3128–3135 (1995).
[CrossRef] [PubMed]

Haake, F.

R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A4(1), 302–313 (1971).
[CrossRef]

Haroche, S.

M. Gross and S. Haroche, “Superradiance: An essay on the theory of collective spontaneous emission,” Phys. Rep.93(5), 301–396 (1982). URL http://www.sciencedirect.com/science/article/pii/0370157382901028 .
[CrossRef]

Heavner, T.

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

Henschel, K.

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A82(3), 033810 (2010).
[CrossRef]

Herman, I. P.

N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke Superradiance in optically pumped HFgGas,” Phys. Rev. Lett.30, 309–312 (1973). URL http://link.aps.org/doi/10.1103/PhysRevLett.30.309 .
[CrossRef]

Higashi, R.

M. Takamoto, F. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature435(7040), 321–324 (2005).
[CrossRef] [PubMed]

Holland, M.

J. Bohnet, Z. Chen, J. Weiner, D. Meiser, M. Holland, and J. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature484(7392), 78–81 (2012).
[CrossRef] [PubMed]

Hong, F.

M. Takamoto, F. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature435(7040), 321–324 (2005).
[CrossRef] [PubMed]

Horak, P.

P. Horak, K. Gheri, and H. Ritsch, “Quantum dynamics of a single-atom cascade laser,” Phys. Rev. A51(4), 3257–3266 (1995).
[CrossRef] [PubMed]

Inouye, S.

S. Inouye, A. Chikkatur, D. Stamper-Kurn, J. Stenger, D. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science285(5427), 571–574 (1999).
[CrossRef] [PubMed]

Jefferts, S.

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

Katori, H.

M. Takamoto, F. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature435(7040), 321–324 (2005).
[CrossRef] [PubMed]

M. Takamoto and H. Katori, “Spectroscopy of the 1S0-3P0 Clock Transition of 87Sr in an optical lattice,” Phys. Rev. Lett.91(22), 223001 (2003).
[CrossRef] [PubMed]

Ketterle, W.

S. Inouye, A. Chikkatur, D. Stamper-Kurn, J. Stenger, D. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science285(5427), 571–574 (1999).
[CrossRef] [PubMed]

Kielich, S.

Z. Ficek, R. Tanaś, and S. Kielich, “Quantum beats and superradiant effects in the spontaneous emission from two nonidentical atoms,” Physica A146(3), 452–482 (1987).
[CrossRef]

Lehmberg, R.

R. Lehmberg, “Radiation from an N-atom system. I. General formalism,” Phys. Rev. A2(3), 883–888 (1970).
[CrossRef]

Lin, G.

G. Lin and S. Yelin, “Superradiance in spin-j particles: effects of multiple levels,” Phys. Rev. A85(3), 033831 (2012).
[CrossRef]

Ludlow, A.

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

MacGillivray, J.

J. MacGillivray and M. Feld, “Theory of superradiance in an extended, optically thick medium,” Rhys. Rv. A14(3), 1169–1189 (1976).

MacGillivray, J. C.

N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke Superradiance in optically pumped HFgGas,” Phys. Rev. Lett.30, 309–312 (1973). URL http://link.aps.org/doi/10.1103/PhysRevLett.30.309 .
[CrossRef]

Majer, J.

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A82(3), 033810 (2010).
[CrossRef]

Martin, M.

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

Meiser, D.

J. Bohnet, Z. Chen, J. Weiner, D. Meiser, M. Holland, and J. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature484(7392), 78–81 (2012).
[CrossRef] [PubMed]

Meystre, P.

M. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. Lett.83(25), 5202–5205 (1999).
[CrossRef]

Moore, M.

M. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. Lett.83(25), 5202–5205 (1999).
[CrossRef]

Parker, T.

G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
[CrossRef]

Pritchard, D.

S. Inouye, A. Chikkatur, D. Stamper-Kurn, J. Stenger, D. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science285(5427), 571–574 (1999).
[CrossRef] [PubMed]

Rehler, N. E.

N. E. Rehler and J. H. Eberly, “Superradiance,” Phys. Rev. A3, 1735–1751 (1971). URL http://link.aps.org/doi/10.1103/PhysRevA.3.1735 .
[CrossRef]

Ritsch, H.

H. Zoubi and H. Ritsch, “Lifetime and emission characteristics of collective electronic excitations in two-dimensional optical lattices,” Phys. Rev. A83(6), 063831 (2011).
[CrossRef]

H. Zoubi and H. Ritsch, “Metastability and directional emission characteristics of excitons in 1D optical lattices,” Europhys. Lett.90, 23001 (2010).
[CrossRef]

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A82(3), 033810 (2010).
[CrossRef]

P. Horak, K. Gheri, and H. Ritsch, “Quantum dynamics of a single-atom cascade laser,” Phys. Rev. A51(4), 3257–3266 (1995).
[CrossRef] [PubMed]

Schmiedmayer, J.

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A82(3), 033810 (2010).
[CrossRef]

Schwendimann, P.

R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A4(1), 302–313 (1971).
[CrossRef]

Skribanowitz, N.

N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke Superradiance in optically pumped HFgGas,” Phys. Rev. Lett.30, 309–312 (1973). URL http://link.aps.org/doi/10.1103/PhysRevLett.30.309 .
[CrossRef]

Stamper-Kurn, D.

S. Inouye, A. Chikkatur, D. Stamper-Kurn, J. Stenger, D. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science285(5427), 571–574 (1999).
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[CrossRef]

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[CrossRef] [PubMed]

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G. Campbell, A. Ludlow, S. Blatt, J. Thomsen, M. Martin, M. de Miranda, T. Zelevinsky, M. Boyd, J. Ye, S. Diddams, T. Heavner, T. Parker, and S. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia45, 539–548 (2008).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Collective spontaneous emission Γij/Γ and resonant dipole-dipole coupling Ωij/Γ for θ = π/2 as a function of inter-atomic distance in units of the resonant wavelength λ0

Fig. 2
Fig. 2

Symmetric exciton state decay rate Γs(N)/Γ as function of atom number for θ = 0 (left) and θ = π/2 (right)

Fig. 3
Fig. 3

Linear chain and triangular array of three atoms with lattice constant a and angle θ

Fig. 4
Fig. 4

Decay scheme (left) and cascade dynamics from |2z〉 state via the single-excitation states |1z〉, |1x〉 and |1y〉 to the ground state for a chain with spacing a = λ0/2

Fig. 5
Fig. 5

Decay from the fully inverted state via |s2〉, |a2〉 (and |b2〉, which due to the degeneracy shows the sam behaviour) and the single-excitation states |s1〉 and |a1〉 (and |b1〉) to the ground state for γ = 0.71Γ (a = λ0/5)

Fig. 6
Fig. 6

Collective decay from fully excited state to the ground state in the equilateral triangle for a = λ0/5 and a = λm/2 (left) and its influence on the maximal Ramsey signal contrast for independent atoms, atoms closely positioned in a triangle as well as in a chain (green) and at magic wavelength-distance (right)

Fig. 7
Fig. 7

Maximum of the energy emission as a function of the number of atoms in the chain for small (left) and large (right) lattice constants a. The distances df and dg refer to the first root of the functions F and G, respectively.

Tables (4)

Tables Icon

Table 1 Collective states (non-normalised) and energy shifts Δ [Hz] for lattice constants a = λ0/2 and a = λm/2. β1 ≈ 1.71, β2 ≈ 1.18 (for a = λ0/2)

Tables Icon

Table 2 [Hz]. Decay (diagonal entries) and feeding rates for the collective states in a chain of lattice constant a = λ0/2

Tables Icon

Table 3 Collective states (non-normalised) in the equilateral triangle with Ω = 3ΓG(k0a)/4

Tables Icon

Table 4 Decay rates (diagonal entries) and feeding rates for the equilateral triangle where we have a uniform collective spontaneous emission rate γ = Γij

Equations (11)

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

ρ ^ t = i h ¯ [ H ^ , ρ ^ ] cd [ ρ ^ ] ,
H ^ = i h ¯ ω 0 S i + S i + i j h ¯ Ω i j S i + S j .
cd [ ρ ^ ] = 1 2 i , j Γ i j ( S i + S j ρ ^ + ρ ^ S i + S j 2 S i ρ ^ S j + )
Γ i j = 3 Γ 2 F ( k 0 r i j ) and Ω i j = 3 Γ 4 G ( k 0 r i j )
F ( ξ ) = ( 1 cos 2 θ ) sin ξ ξ + ( 1 3 cos 2 θ ) ( cos ξ ξ 2 sin ξ ξ 3 ) , G ( ξ ) = ( 1 cos 2 θ ) cos ξ ξ + ( 1 3 cos 2 θ ) ( sin ξ ξ 2 + cos ξ ξ 3 ) ,
H ^ = k h ¯ ω k S k + S k ,
i , j Γ i j S i + S j | e e | = i , j Γ i j δ i j | e e | = i Γ i i | e e | = Γ e | e e | .
| s = 1 N i = 1 N | g 1 e i g n ,
Γ s ( N ) = Γ [ 1 + 2 n = 1 N 1 ( 1 n N ) F ( k 0 a n ) ] .
λ m 2 λ 0 0.5824 .
ρ interm ( t ) = A [ 1 exp ( ν t ) ] ] exp ( γ t ) ,

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