Abstract

We investigate the fluorescence spectrum of a two-level atom in a cavity when the atom is driven by a classical field. We show that forbidden dipole transitions in the Jaynes–Cummings ladder structure are induced in the presence of cavity damping, which deteriorates the degree of otherwise perfect destructive interference among the transition channels. With the larger cavity decay, these transitions are more enhanced.

© 2001 Optical Society of America

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References

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  1. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
    [CrossRef]
  2. P. R. Berman, ed., Cavity Quantum Electrodynamics (Academic, New York, 1994).
  3. A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Science 288, 2024 (2000).
    [CrossRef] [PubMed]
  4. R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
    [CrossRef] [PubMed]
  5. J. J. Childs, K. An, M. S. Otteson, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 77, 2901 (1996).
    [CrossRef] [PubMed]
  6. M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).
    [CrossRef] [PubMed]
  7. P. W. Pinkse, T. Fischer, P. Maunz, and G. Rempe, Nature 404, 365 (2000).
    [CrossRef] [PubMed]
  8. J. Ye, D. Vernooy, and H. J. Kimble, Phys. Rev. Lett. 83, 4987 (1999).
    [CrossRef]
  9. H. Nha, Y.-T. Chough, and K. An, Phys. Rev. A 62, 21801(R) (2000).
    [CrossRef]
  10. P. Alsing, D.-S. Guo, and H. J. Carmichael, Phys. Rev. A 45, 5135 (1992).
    [CrossRef] [PubMed]
  11. The states |ϕn±〉 have the various frequency components in the Schrödinger picture given by mω0±gn, where m, n are arbitrary integers n≥0. The dipole transitions, however, are always of the type Δm=1, so the emitted photons have the frequencies ω0±gn.
  12. P. Alsing, D. A. Cardimona, and H. J. Carmichael, Phys. Rev. A 45, 1793 (1992).
    [CrossRef] [PubMed]
  13. R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford U. Press, Cambridge, 1983).

2000 (3)

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Science 288, 2024 (2000).
[CrossRef] [PubMed]

P. W. Pinkse, T. Fischer, P. Maunz, and G. Rempe, Nature 404, 365 (2000).
[CrossRef] [PubMed]

H. Nha, Y.-T. Chough, and K. An, Phys. Rev. A 62, 21801(R) (2000).
[CrossRef]

1999 (1)

J. Ye, D. Vernooy, and H. J. Kimble, Phys. Rev. Lett. 83, 4987 (1999).
[CrossRef]

1996 (2)

J. J. Childs, K. An, M. S. Otteson, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 77, 2901 (1996).
[CrossRef] [PubMed]

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).
[CrossRef] [PubMed]

1992 (3)

R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

P. Alsing, D.-S. Guo, and H. J. Carmichael, Phys. Rev. A 45, 5135 (1992).
[CrossRef] [PubMed]

P. Alsing, D. A. Cardimona, and H. J. Carmichael, Phys. Rev. A 45, 1793 (1992).
[CrossRef] [PubMed]

1963 (1)

E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[CrossRef]

Alsing, P.

P. Alsing, D. A. Cardimona, and H. J. Carmichael, Phys. Rev. A 45, 1793 (1992).
[CrossRef] [PubMed]

P. Alsing, D.-S. Guo, and H. J. Carmichael, Phys. Rev. A 45, 5135 (1992).
[CrossRef] [PubMed]

An, K.

H. Nha, Y.-T. Chough, and K. An, Phys. Rev. A 62, 21801(R) (2000).
[CrossRef]

J. J. Childs, K. An, M. S. Otteson, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 77, 2901 (1996).
[CrossRef] [PubMed]

Bertet, P.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Science 288, 2024 (2000).
[CrossRef] [PubMed]

Brune, M.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Science 288, 2024 (2000).
[CrossRef] [PubMed]

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).
[CrossRef] [PubMed]

Cardimona, D. A.

P. Alsing, D. A. Cardimona, and H. J. Carmichael, Phys. Rev. A 45, 1793 (1992).
[CrossRef] [PubMed]

Carmichael, H. J.

P. Alsing, D. A. Cardimona, and H. J. Carmichael, Phys. Rev. A 45, 1793 (1992).
[CrossRef] [PubMed]

P. Alsing, D.-S. Guo, and H. J. Carmichael, Phys. Rev. A 45, 5135 (1992).
[CrossRef] [PubMed]

Childs, J. J.

J. J. Childs, K. An, M. S. Otteson, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 77, 2901 (1996).
[CrossRef] [PubMed]

Chough, Y.-T.

H. Nha, Y.-T. Chough, and K. An, Phys. Rev. A 62, 21801(R) (2000).
[CrossRef]

Cummings, F. W.

E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[CrossRef]

Dasari, R. R.

J. J. Childs, K. An, M. S. Otteson, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 77, 2901 (1996).
[CrossRef] [PubMed]

Dreyer, J.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).
[CrossRef] [PubMed]

Feld, M. S.

J. J. Childs, K. An, M. S. Otteson, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 77, 2901 (1996).
[CrossRef] [PubMed]

Fischer, T.

P. W. Pinkse, T. Fischer, P. Maunz, and G. Rempe, Nature 404, 365 (2000).
[CrossRef] [PubMed]

Guo, D.-S.

P. Alsing, D.-S. Guo, and H. J. Carmichael, Phys. Rev. A 45, 5135 (1992).
[CrossRef] [PubMed]

Hagley, E.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).
[CrossRef] [PubMed]

Haroche, S.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Science 288, 2024 (2000).
[CrossRef] [PubMed]

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).
[CrossRef] [PubMed]

Jaynes, E. T.

E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[CrossRef]

Kimble, H. J.

J. Ye, D. Vernooy, and H. J. Kimble, Phys. Rev. Lett. 83, 4987 (1999).
[CrossRef]

R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford U. Press, Cambridge, 1983).

Maali, A.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).
[CrossRef] [PubMed]

Maunz, P.

P. W. Pinkse, T. Fischer, P. Maunz, and G. Rempe, Nature 404, 365 (2000).
[CrossRef] [PubMed]

Nha, H.

H. Nha, Y.-T. Chough, and K. An, Phys. Rev. A 62, 21801(R) (2000).
[CrossRef]

Nogues, G.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Science 288, 2024 (2000).
[CrossRef] [PubMed]

Osnaghi, S.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Science 288, 2024 (2000).
[CrossRef] [PubMed]

Otteson, M. S.

J. J. Childs, K. An, M. S. Otteson, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 77, 2901 (1996).
[CrossRef] [PubMed]

Pinkse, P. W.

P. W. Pinkse, T. Fischer, P. Maunz, and G. Rempe, Nature 404, 365 (2000).
[CrossRef] [PubMed]

Raimond, J.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Science 288, 2024 (2000).
[CrossRef] [PubMed]

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).
[CrossRef] [PubMed]

Rauschenbeutel, A.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Science 288, 2024 (2000).
[CrossRef] [PubMed]

Rempe, G.

P. W. Pinkse, T. Fischer, P. Maunz, and G. Rempe, Nature 404, 365 (2000).
[CrossRef] [PubMed]

R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

Schmidt-Kaler, F.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).
[CrossRef] [PubMed]

Thompson, R. J.

R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

Vernooy, D.

J. Ye, D. Vernooy, and H. J. Kimble, Phys. Rev. Lett. 83, 4987 (1999).
[CrossRef]

Ye, J.

J. Ye, D. Vernooy, and H. J. Kimble, Phys. Rev. Lett. 83, 4987 (1999).
[CrossRef]

Nature (1)

P. W. Pinkse, T. Fischer, P. Maunz, and G. Rempe, Nature 404, 365 (2000).
[CrossRef] [PubMed]

Phys. Rev. A (3)

H. Nha, Y.-T. Chough, and K. An, Phys. Rev. A 62, 21801(R) (2000).
[CrossRef]

P. Alsing, D.-S. Guo, and H. J. Carmichael, Phys. Rev. A 45, 5135 (1992).
[CrossRef] [PubMed]

P. Alsing, D. A. Cardimona, and H. J. Carmichael, Phys. Rev. A 45, 1793 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

J. Ye, D. Vernooy, and H. J. Kimble, Phys. Rev. Lett. 83, 4987 (1999).
[CrossRef]

R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

J. J. Childs, K. An, M. S. Otteson, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 77, 2901 (1996).
[CrossRef] [PubMed]

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).
[CrossRef] [PubMed]

Proc. IEEE (1)

E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[CrossRef]

Science (1)

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. Raimond, and S. Haroche, Science 288, 2024 (2000).
[CrossRef] [PubMed]

Other (3)

R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford U. Press, Cambridge, 1983).

P. R. Berman, ed., Cavity Quantum Electrodynamics (Academic, New York, 1994).

The states |ϕn±〉 have the various frequency components in the Schrödinger picture given by mω0±gn, where m, n are arbitrary integers n≥0. The dipole transitions, however, are always of the type Δm=1, so the emitted photons have the frequencies ω0±gn.

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Figures (1)

Fig. 1
Fig. 1

Power spectrum of the atomic fluorescence, normalized to the total integrated intensity (on a log scale). (a) Ω/g=8/3, 2κ/g=0.03; (b) Ω/g=16/3, 2κ/g=0.03; (c) Ω/g=8/3, 2κ/g=0.1. The locations of the peaks are identified as ag, b2g, c2g, d2-1g, with g=g1-2Ωκ/g223/4. The relative strengths of lines a, b, and c are roughly 300:1.04:1, 100:1.16:1, and 50:1.21:1 (on a linear scale) in (a), (b), and (c), respectively.

Equations (13)

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HI=igaσ--aσ++Hd,
Hd=iΩσ+-σ-.
Hd=iEa-a,
En±=±ng,n=0,1,2,,
|ϕ0=Dα|0|-,|ϕn±=Dα1/2[|n-1|+±i|n|-],
En±=±ng1-2E/g23/4±ng,
ϕnξσ-ϕnξ=iξδn,n-1,
ρ·I=ga+σ--aσ++Ωσ+-σ-,ρI+γ/22σ-ρIσ+-σ+σ-ρI-ρIσ+σ-+κ2aρIa+-a+aρI-ρIa+a,
ρ˜·=ga+σ--aσ+,ρ˜+Ωκga+-a,ρ˜+γ/22σ-ρ˜σ+-σ+σ-ρ˜-ρ˜σ+σ-+κ2aρ˜a+-a+aρ˜-ρ˜a+a.
Heff=iga+σ--aσ++iΩκga+-a.
En±=±ng1-2Ωκ/g223/4,n=0,1,2,,
χ0σ-χ2+2=2Ωκ/g22.
ϕ0σ-ϕ2+=α-i20,-σ-0,++i21,-σ-1,++Oα2+=0.

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