Abstract

A microscopic analysis is presented for the extreme nonlinear optical response of semiconductor quantum wells and wires after intense excitation with femtosecond laser pulses. In this regime, the light–matter interaction is the dominant eneregy scale, leading to a number of interesting effects such as carrier-wave Rabi flopping, Mollow splitting, and the creation of higher harmonics. The results presented here were obtained by evaluating the semiconductor Bloch equations without the rotating wave approximation. The electronic dispersion of semiconductor nanostructures is shown to have a characteristic influence on the extreme nonlinear optical response, whereas the relative importance of the carrier Coulomb interaction decreases with increasing excitation intensities.

© 2006 Optical Society of America

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References

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  1. M. Wegener, Extreme Nonlinear Optics (Springer, 2005).
  2. T. Brabec and F. Krausz, 'Intense few-cycle laser fields: frontiers of nonlinear optics,' Rev. Mod. Phys. 72, 545-591 (2000).
    [CrossRef]
  3. N. Bloembergen, Nonlinear Optics (Benjamin, 1965).
  4. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1975).
  5. S. Hughes, 'Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,' Phys. Rev. Lett. 81, 3363-3366 (1998).
    [CrossRef]
  6. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Signatures of carrier-wave Rabi flopping in GaAs,' Phys. Rev. Lett. 87, 057401 (2001).
    [CrossRef] [PubMed]
  7. T. Tritschler, O. D. Mücke, and M. Wegener, 'Extreme nonlinear optics of two-level systems,' Phys. Rev. A 68, 033404 (2003).
    [CrossRef]
  8. T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, 'Evidence of third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,' Phys. Rev. Lett. 90, 217404 (2003).
    [CrossRef] [PubMed]
  9. Q. T. Vu, H. Haug, O. D. Mücke, T. Tritschler, M. Wegener, G. Khitrova, and H. M. Gibbs, 'Light-induced gaps in semiconductor band-to-band transitions,' Phys. Rev. Lett. 92, 217403 (2004).
    [CrossRef] [PubMed]
  10. R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, 'Ultrafast pulse interactions with two-level atoms,' Phys. Rev. A 52, 3082-3094 (1995).
    [CrossRef] [PubMed]
  11. V. P. Kalosha and J. Herrmann, 'Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,' Phys. Rev. Lett. 83, 544-547 (1999).
    [CrossRef]
  12. S. Hughes, 'Subfemtosecond soft-x-ray generation from a two-level atom: extreme carrier-wave Rabi flopping,' Phys. Rev. A 62, 055401 (2000).
    [CrossRef]
  13. X. Song, S. Gong, W. Yang, and Z. Hu, 'Propagation of an attosecond pulse in a dense two-level medium,' Phys. Rev. A 70, 013817 (2004).
    [CrossRef]
  14. R. Parzynsky and M. Sobczak, 'Analytical calculation of atomic response to a few-cycle optical pulse,' J. Phys. B 37, 743-751 (2004).
    [CrossRef]
  15. J. Cheng and J. Zhou, 'Validity of the two-level approximation in the interaction of few-cycle light pulses with atoms,' Phys. Rev. A 67, 041404 (2003).
    [CrossRef]
  16. X. Song, S. Gong, R. Li, and Z. Hu, 'Effect of time-dependent ionization on the propagation of a few-cycle laser pulse in a two-level medium,' Phys. Rev. A 72, 043820 (2005).
    [CrossRef]
  17. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,' Phys. Rev. Lett. 89, 127401 (2002).
    [CrossRef] [PubMed]
  18. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).
  19. W. Schäfer and M. Wegener, Semiconductor Optics and Transport Phenomena (Springer, 2002).
  20. Q. T. Vu and H. Haug, 'Detection of light-induced band gaps by ultrafast femtosecond pump and probe spectroscopy,' Phys. Rev. B 71, 035305 (2005).
    [CrossRef]
  21. M. Lindberg and S. W. Koch, 'Effective Bloch equations for semiconductors,' Phys. Rev. B 38, 3342-3350 (1988).
    [CrossRef]
  22. L. Bányai, I. Galbraith, C. Ell, and H. Haug, 'Excitons and biexcitons in semiconductor quantum wires,' Phys. Rev. B 36, 6099-6104 (1987).
    [CrossRef]
  23. W. Schäfer, 'Influence of electron-electron scattering on femtosecond four-wave mixing in semiconductors,' J. Opt. Soc. Am. B 13, 1291-1297 (1996).
    [CrossRef]
  24. B. R. Mollow, 'Power spectrum of light scattered by two-level systems,' Phys. Rev. 188, 1969-1975 (1969).
    [CrossRef]

2005 (2)

X. Song, S. Gong, R. Li, and Z. Hu, 'Effect of time-dependent ionization on the propagation of a few-cycle laser pulse in a two-level medium,' Phys. Rev. A 72, 043820 (2005).
[CrossRef]

Q. T. Vu and H. Haug, 'Detection of light-induced band gaps by ultrafast femtosecond pump and probe spectroscopy,' Phys. Rev. B 71, 035305 (2005).
[CrossRef]

2004 (3)

X. Song, S. Gong, W. Yang, and Z. Hu, 'Propagation of an attosecond pulse in a dense two-level medium,' Phys. Rev. A 70, 013817 (2004).
[CrossRef]

R. Parzynsky and M. Sobczak, 'Analytical calculation of atomic response to a few-cycle optical pulse,' J. Phys. B 37, 743-751 (2004).
[CrossRef]

Q. T. Vu, H. Haug, O. D. Mücke, T. Tritschler, M. Wegener, G. Khitrova, and H. M. Gibbs, 'Light-induced gaps in semiconductor band-to-band transitions,' Phys. Rev. Lett. 92, 217403 (2004).
[CrossRef] [PubMed]

2003 (3)

T. Tritschler, O. D. Mücke, and M. Wegener, 'Extreme nonlinear optics of two-level systems,' Phys. Rev. A 68, 033404 (2003).
[CrossRef]

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, 'Evidence of third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,' Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

J. Cheng and J. Zhou, 'Validity of the two-level approximation in the interaction of few-cycle light pulses with atoms,' Phys. Rev. A 67, 041404 (2003).
[CrossRef]

2002 (1)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,' Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

2001 (1)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Signatures of carrier-wave Rabi flopping in GaAs,' Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

2000 (2)

T. Brabec and F. Krausz, 'Intense few-cycle laser fields: frontiers of nonlinear optics,' Rev. Mod. Phys. 72, 545-591 (2000).
[CrossRef]

S. Hughes, 'Subfemtosecond soft-x-ray generation from a two-level atom: extreme carrier-wave Rabi flopping,' Phys. Rev. A 62, 055401 (2000).
[CrossRef]

1999 (1)

V. P. Kalosha and J. Herrmann, 'Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,' Phys. Rev. Lett. 83, 544-547 (1999).
[CrossRef]

1998 (1)

S. Hughes, 'Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,' Phys. Rev. Lett. 81, 3363-3366 (1998).
[CrossRef]

1996 (1)

1995 (1)

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, 'Ultrafast pulse interactions with two-level atoms,' Phys. Rev. A 52, 3082-3094 (1995).
[CrossRef] [PubMed]

1988 (1)

M. Lindberg and S. W. Koch, 'Effective Bloch equations for semiconductors,' Phys. Rev. B 38, 3342-3350 (1988).
[CrossRef]

1987 (1)

L. Bányai, I. Galbraith, C. Ell, and H. Haug, 'Excitons and biexcitons in semiconductor quantum wires,' Phys. Rev. B 36, 6099-6104 (1987).
[CrossRef]

1969 (1)

B. R. Mollow, 'Power spectrum of light scattered by two-level systems,' Phys. Rev. 188, 1969-1975 (1969).
[CrossRef]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1975).

Arnold, J. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, 'Ultrafast pulse interactions with two-level atoms,' Phys. Rev. A 52, 3082-3094 (1995).
[CrossRef] [PubMed]

Bányai, L.

L. Bányai, I. Galbraith, C. Ell, and H. Haug, 'Excitons and biexcitons in semiconductor quantum wires,' Phys. Rev. B 36, 6099-6104 (1987).
[CrossRef]

Bloembergen, N.

N. Bloembergen, Nonlinear Optics (Benjamin, 1965).

Brabec, T.

T. Brabec and F. Krausz, 'Intense few-cycle laser fields: frontiers of nonlinear optics,' Rev. Mod. Phys. 72, 545-591 (2000).
[CrossRef]

Cheng, J.

J. Cheng and J. Zhou, 'Validity of the two-level approximation in the interaction of few-cycle light pulses with atoms,' Phys. Rev. A 67, 041404 (2003).
[CrossRef]

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1975).

Ell, C.

L. Bányai, I. Galbraith, C. Ell, and H. Haug, 'Excitons and biexcitons in semiconductor quantum wires,' Phys. Rev. B 36, 6099-6104 (1987).
[CrossRef]

Galbraith, I.

L. Bányai, I. Galbraith, C. Ell, and H. Haug, 'Excitons and biexcitons in semiconductor quantum wires,' Phys. Rev. B 36, 6099-6104 (1987).
[CrossRef]

Gibbs, H. M.

Q. T. Vu, H. Haug, O. D. Mücke, T. Tritschler, M. Wegener, G. Khitrova, and H. M. Gibbs, 'Light-induced gaps in semiconductor band-to-band transitions,' Phys. Rev. Lett. 92, 217403 (2004).
[CrossRef] [PubMed]

Gogny, D. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, 'Ultrafast pulse interactions with two-level atoms,' Phys. Rev. A 52, 3082-3094 (1995).
[CrossRef] [PubMed]

Gong, S.

X. Song, S. Gong, R. Li, and Z. Hu, 'Effect of time-dependent ionization on the propagation of a few-cycle laser pulse in a two-level medium,' Phys. Rev. A 72, 043820 (2005).
[CrossRef]

X. Song, S. Gong, W. Yang, and Z. Hu, 'Propagation of an attosecond pulse in a dense two-level medium,' Phys. Rev. A 70, 013817 (2004).
[CrossRef]

Haug, H.

Q. T. Vu and H. Haug, 'Detection of light-induced band gaps by ultrafast femtosecond pump and probe spectroscopy,' Phys. Rev. B 71, 035305 (2005).
[CrossRef]

Q. T. Vu, H. Haug, O. D. Mücke, T. Tritschler, M. Wegener, G. Khitrova, and H. M. Gibbs, 'Light-induced gaps in semiconductor band-to-band transitions,' Phys. Rev. Lett. 92, 217403 (2004).
[CrossRef] [PubMed]

L. Bányai, I. Galbraith, C. Ell, and H. Haug, 'Excitons and biexcitons in semiconductor quantum wires,' Phys. Rev. B 36, 6099-6104 (1987).
[CrossRef]

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).

Herrmann, J.

V. P. Kalosha and J. Herrmann, 'Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,' Phys. Rev. Lett. 83, 544-547 (1999).
[CrossRef]

Hu, Z.

X. Song, S. Gong, R. Li, and Z. Hu, 'Effect of time-dependent ionization on the propagation of a few-cycle laser pulse in a two-level medium,' Phys. Rev. A 72, 043820 (2005).
[CrossRef]

X. Song, S. Gong, W. Yang, and Z. Hu, 'Propagation of an attosecond pulse in a dense two-level medium,' Phys. Rev. A 70, 013817 (2004).
[CrossRef]

Hughes, S.

S. Hughes, 'Subfemtosecond soft-x-ray generation from a two-level atom: extreme carrier-wave Rabi flopping,' Phys. Rev. A 62, 055401 (2000).
[CrossRef]

S. Hughes, 'Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,' Phys. Rev. Lett. 81, 3363-3366 (1998).
[CrossRef]

Kalosha, V. P.

V. P. Kalosha and J. Herrmann, 'Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,' Phys. Rev. Lett. 83, 544-547 (1999).
[CrossRef]

Kärtner, F. X.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, 'Evidence of third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,' Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,' Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Signatures of carrier-wave Rabi flopping in GaAs,' Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

Khitrova, G.

Q. T. Vu, H. Haug, O. D. Mücke, T. Tritschler, M. Wegener, G. Khitrova, and H. M. Gibbs, 'Light-induced gaps in semiconductor band-to-band transitions,' Phys. Rev. Lett. 92, 217403 (2004).
[CrossRef] [PubMed]

Koch, S. W.

M. Lindberg and S. W. Koch, 'Effective Bloch equations for semiconductors,' Phys. Rev. B 38, 3342-3350 (1988).
[CrossRef]

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).

Krausz, F.

T. Brabec and F. Krausz, 'Intense few-cycle laser fields: frontiers of nonlinear optics,' Rev. Mod. Phys. 72, 545-591 (2000).
[CrossRef]

Li, R.

X. Song, S. Gong, R. Li, and Z. Hu, 'Effect of time-dependent ionization on the propagation of a few-cycle laser pulse in a two-level medium,' Phys. Rev. A 72, 043820 (2005).
[CrossRef]

Lindberg, M.

M. Lindberg and S. W. Koch, 'Effective Bloch equations for semiconductors,' Phys. Rev. B 38, 3342-3350 (1988).
[CrossRef]

Mollow, B. R.

B. R. Mollow, 'Power spectrum of light scattered by two-level systems,' Phys. Rev. 188, 1969-1975 (1969).
[CrossRef]

Morgner, U.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, 'Evidence of third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,' Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,' Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Signatures of carrier-wave Rabi flopping in GaAs,' Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

Mücke, O. D.

Q. T. Vu, H. Haug, O. D. Mücke, T. Tritschler, M. Wegener, G. Khitrova, and H. M. Gibbs, 'Light-induced gaps in semiconductor band-to-band transitions,' Phys. Rev. Lett. 92, 217403 (2004).
[CrossRef] [PubMed]

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, 'Evidence of third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,' Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

T. Tritschler, O. D. Mücke, and M. Wegener, 'Extreme nonlinear optics of two-level systems,' Phys. Rev. A 68, 033404 (2003).
[CrossRef]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,' Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Signatures of carrier-wave Rabi flopping in GaAs,' Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

Parzynsky, R.

R. Parzynsky and M. Sobczak, 'Analytical calculation of atomic response to a few-cycle optical pulse,' J. Phys. B 37, 743-751 (2004).
[CrossRef]

Schäfer, W.

Sobczak, M.

R. Parzynsky and M. Sobczak, 'Analytical calculation of atomic response to a few-cycle optical pulse,' J. Phys. B 37, 743-751 (2004).
[CrossRef]

Song, X.

X. Song, S. Gong, R. Li, and Z. Hu, 'Effect of time-dependent ionization on the propagation of a few-cycle laser pulse in a two-level medium,' Phys. Rev. A 72, 043820 (2005).
[CrossRef]

X. Song, S. Gong, W. Yang, and Z. Hu, 'Propagation of an attosecond pulse in a dense two-level medium,' Phys. Rev. A 70, 013817 (2004).
[CrossRef]

Tritschler, T.

Q. T. Vu, H. Haug, O. D. Mücke, T. Tritschler, M. Wegener, G. Khitrova, and H. M. Gibbs, 'Light-induced gaps in semiconductor band-to-band transitions,' Phys. Rev. Lett. 92, 217403 (2004).
[CrossRef] [PubMed]

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, 'Evidence of third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,' Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

T. Tritschler, O. D. Mücke, and M. Wegener, 'Extreme nonlinear optics of two-level systems,' Phys. Rev. A 68, 033404 (2003).
[CrossRef]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,' Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Signatures of carrier-wave Rabi flopping in GaAs,' Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

Vu, Q. T.

Q. T. Vu and H. Haug, 'Detection of light-induced band gaps by ultrafast femtosecond pump and probe spectroscopy,' Phys. Rev. B 71, 035305 (2005).
[CrossRef]

Q. T. Vu, H. Haug, O. D. Mücke, T. Tritschler, M. Wegener, G. Khitrova, and H. M. Gibbs, 'Light-induced gaps in semiconductor band-to-band transitions,' Phys. Rev. Lett. 92, 217403 (2004).
[CrossRef] [PubMed]

Wegener, M.

Q. T. Vu, H. Haug, O. D. Mücke, T. Tritschler, M. Wegener, G. Khitrova, and H. M. Gibbs, 'Light-induced gaps in semiconductor band-to-band transitions,' Phys. Rev. Lett. 92, 217403 (2004).
[CrossRef] [PubMed]

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, 'Evidence of third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,' Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

T. Tritschler, O. D. Mücke, and M. Wegener, 'Extreme nonlinear optics of two-level systems,' Phys. Rev. A 68, 033404 (2003).
[CrossRef]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,' Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Signatures of carrier-wave Rabi flopping in GaAs,' Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

W. Schäfer and M. Wegener, Semiconductor Optics and Transport Phenomena (Springer, 2002).

M. Wegener, Extreme Nonlinear Optics (Springer, 2005).

Yang, W.

X. Song, S. Gong, W. Yang, and Z. Hu, 'Propagation of an attosecond pulse in a dense two-level medium,' Phys. Rev. A 70, 013817 (2004).
[CrossRef]

Zhou, J.

J. Cheng and J. Zhou, 'Validity of the two-level approximation in the interaction of few-cycle light pulses with atoms,' Phys. Rev. A 67, 041404 (2003).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, 'Ultrafast pulse interactions with two-level atoms,' Phys. Rev. A 52, 3082-3094 (1995).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

R. Parzynsky and M. Sobczak, 'Analytical calculation of atomic response to a few-cycle optical pulse,' J. Phys. B 37, 743-751 (2004).
[CrossRef]

Phys. Rev. (1)

B. R. Mollow, 'Power spectrum of light scattered by two-level systems,' Phys. Rev. 188, 1969-1975 (1969).
[CrossRef]

Phys. Rev. A (6)

J. Cheng and J. Zhou, 'Validity of the two-level approximation in the interaction of few-cycle light pulses with atoms,' Phys. Rev. A 67, 041404 (2003).
[CrossRef]

X. Song, S. Gong, R. Li, and Z. Hu, 'Effect of time-dependent ionization on the propagation of a few-cycle laser pulse in a two-level medium,' Phys. Rev. A 72, 043820 (2005).
[CrossRef]

S. Hughes, 'Subfemtosecond soft-x-ray generation from a two-level atom: extreme carrier-wave Rabi flopping,' Phys. Rev. A 62, 055401 (2000).
[CrossRef]

X. Song, S. Gong, W. Yang, and Z. Hu, 'Propagation of an attosecond pulse in a dense two-level medium,' Phys. Rev. A 70, 013817 (2004).
[CrossRef]

T. Tritschler, O. D. Mücke, and M. Wegener, 'Extreme nonlinear optics of two-level systems,' Phys. Rev. A 68, 033404 (2003).
[CrossRef]

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, 'Ultrafast pulse interactions with two-level atoms,' Phys. Rev. A 52, 3082-3094 (1995).
[CrossRef] [PubMed]

Phys. Rev. B (3)

Q. T. Vu and H. Haug, 'Detection of light-induced band gaps by ultrafast femtosecond pump and probe spectroscopy,' Phys. Rev. B 71, 035305 (2005).
[CrossRef]

M. Lindberg and S. W. Koch, 'Effective Bloch equations for semiconductors,' Phys. Rev. B 38, 3342-3350 (1988).
[CrossRef]

L. Bányai, I. Galbraith, C. Ell, and H. Haug, 'Excitons and biexcitons in semiconductor quantum wires,' Phys. Rev. B 36, 6099-6104 (1987).
[CrossRef]

Phys. Rev. Lett. (6)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,' Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

V. P. Kalosha and J. Herrmann, 'Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,' Phys. Rev. Lett. 83, 544-547 (1999).
[CrossRef]

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, 'Evidence of third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,' Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

Q. T. Vu, H. Haug, O. D. Mücke, T. Tritschler, M. Wegener, G. Khitrova, and H. M. Gibbs, 'Light-induced gaps in semiconductor band-to-band transitions,' Phys. Rev. Lett. 92, 217403 (2004).
[CrossRef] [PubMed]

S. Hughes, 'Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,' Phys. Rev. Lett. 81, 3363-3366 (1998).
[CrossRef]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, 'Signatures of carrier-wave Rabi flopping in GaAs,' Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, 'Intense few-cycle laser fields: frontiers of nonlinear optics,' Rev. Mod. Phys. 72, 545-591 (2000).
[CrossRef]

Other (5)

N. Bloembergen, Nonlinear Optics (Benjamin, 1965).

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1975).

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).

W. Schäfer and M. Wegener, Semiconductor Optics and Transport Phenomena (Springer, 2002).

M. Wegener, Extreme Nonlinear Optics (Springer, 2005).

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Figures (9)

Fig. 1
Fig. 1

Intensity of the emitted radiation I rad of a two-level system as a function of the spectrometer frequency ω and the peak Rabi frequency ω R . I rad is plotted on a logarithmic scale that spans 7 orders of magnitude. The system is excited resonantly by a Gaussian laser pulse with a duration of τ = 10 fs . The transition energy of the system is E 2 L S = ω 0 = 1.43 eV .

Fig. 2
Fig. 2

Intensity of the emitted radiation I rad of a 1D semiconductor quantum wire described by a two-band effective mass model with an energy gap of E G = ω 0 = 1.43 eV . (a) Free-carrier result, i.e., the many-body Coulomb interaction is neglected, (b) the Coulomb interaction is treated on the Hartree–Fock level. The excitation parameters are the same as in Fig. 1.

Fig. 3
Fig. 3

Same as Fig. 1 but for nonresonant excitation of a two-level system with a transition energy of E 2 LS = 1.4 ω 0 2 eV .

Fig. 4
Fig. 4

Same as Fig. 2a computed for a 2D semiconductor quantum well.

Fig. 5
Fig. 5

Cross sections through Fig. 2a (dotted curves, free-carrier calculation) and Fig. 2b (solid curves, Hartree–Fock calculation) for two different Rabi frequencies.

Fig. 6
Fig. 6

Intensity of the emitted radiation I rad for smaller Rabi frequencies at approximately ω ω 0 = 1 for (a) two-level system, (b) free-carrier, and (c) Hartree–Fock calculation. The excitation conditions are the same as in Figs. 1, 2. Note that the axes are scaled in units of the 3D exciton binding energy E B 4.37 meV , which is approximately 327 times smaller than the transition energy of the two-level system, and the bandgap ω 0 = E G = 1.43 eV .

Fig. 7
Fig. 7

Same as Fig. 5 but the calculations are performed on the Hartree–Fock level (dotted curve) and on the second-Born level (solid curve).

Fig. 8
Fig. 8

Spectra of the emitted radiation I rad computed on the Hartree–Fock level for ω R = 0.5 ω 0 . (a) Results for the dephasing times of T 2 = 50 fs (solid curve) and T 2 = 30 fs (dotted curve) are shown. The pulse duration is fixed at τ = 10 fs here. (b) Spectra for different pulse durations, i.e., τ = 20 fs (dotted curve), and τ = 10 fs (solid curve).

Fig. 9
Fig. 9

Intensity of the emitted radiation I rad of a resonantly excited two-level system obtained from the analytical solution of Eq. (13) for a box-shaped pulse and in RWA. The dephasing time is T 2 = 50 fs , and the pulse duration is (a) τ = 10 fs and (b) τ = 5 fs .

Equations (14)

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t p k = i ( ϵ k e + ϵ k h ) p k + i ( 1 n k e n k h ) ω R , k + t p k corr ,
t n k e = 2 Im [ ω R , k p k * ] + t n k e corr ,
t n k h = 2 Im [ ω R , k p k * ] + t n k h corr .
ω R , k = 1 ( d k E ( t ) + q k V k q p q ) ,
ϵ k e , h = E k e , h q k V k q n q e , h .
d k = d 0 E G E k e + E k h ,
V q 2 D = e 2 2 ϵ 0 ϵ r A 1 q ,
V q 1 D ( z ) = e 2 4 π ϵ 0 ϵ r 1 z + α R ,
t p k corr = p k T 2 ,
P ( t ) = k ( d k p k + c.c. ) .
E ( t ) = E 0 exp [ 2 ln ( 2 ) t 2 τ 2 ] cos ( ω 0 t ) ,
P ( t , ω R ) = { i 2 sin ( ω R t ) e i ω 0 t e ( t T 2 ) , t τ i 2 sin ( ω R τ ) e i ω 0 t e ( t T 2 ) , t τ .
P ( Δ ω , ω R ) = i 2 1 ( i Δ ω T 2 1 ) 2 + ω R 2 { e ( i Δ ω T 2 1 ) τ [ ( i Δ ω T 2 1 ) sin ( ω R τ ) ω R cos ( ω R τ ) ] + ω R } i 2 sin ( ω R τ ) i Δ ω T 2 1 e ( i Δ ω T 2 1 ) τ ,
P ( 0 , ω R ) = i 2 ω R T 2 2 ( ω R T 2 ) 2 + 1 { 1 e τ T 2 [ cos ( ω R τ ) ω R T 2 sin ( ω R τ ) ] } .

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