Abstract

We have studied the ionization of Rydberg atoms by few-cycle radio-frequency pulses and used two-color fields to control the ionization dynamics. We show that the number of times that electrons are emitted during a pulse can be limited and that the duration of the electron emission can be shortened. These results, once they are transposed to the optical domain, may inspire new strategies for the production of single attosecond pulses.

© 2004 Optical Society of America

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  1. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
    [Crossref] [PubMed]
  2. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
    [Crossref] [PubMed]
  3. S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, Phys. Rev. Lett. 91, 223902 (2003).
    [Crossref]
  4. P. B. Corkum, Phys. Rev. Lett. 71, 1995 (1993).
    [Crossref]
  5. H. Niikura, F. Legare, R. Hasbani, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, Nature 421, 826 (2003).
    [Crossref] [PubMed]
  6. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
    [Crossref] [PubMed]
  7. A. Gürtler, F. Robicheaux, M. J. J. Vrakking, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 063901 (2004).
    [Crossref]
  8. R. J. Damburg and V. V. Kolosov, J. Phys. B 12, 2637 (1979).
    [Crossref]
  9. L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Pergamon, Oxford, 1977), p. 1974.
  10. M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1987)].
  11. As the field is symmetric near t=0, one would also expect the ionization signal to be symmetric. However, as we keep the pulse energy constant, variations in the pulse parameters lead to high field values that deplete the population in the Rydberg states significantly, leading to the asymmetry observed in the figures.
  12. P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, Opt. Lett. 19, 1870 (1994).
    [Crossref]

2004 (1)

A. Gürtler, F. Robicheaux, M. J. J. Vrakking, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 063901 (2004).
[Crossref]

2003 (2)

H. Niikura, F. Legare, R. Hasbani, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, Nature 421, 826 (2003).
[Crossref] [PubMed]

S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, Phys. Rev. Lett. 91, 223902 (2003).
[Crossref]

2001 (2)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[Crossref] [PubMed]

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

1994 (2)

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[Crossref] [PubMed]

P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, Opt. Lett. 19, 1870 (1994).
[Crossref]

1993 (1)

P. B. Corkum, Phys. Rev. Lett. 71, 1995 (1993).
[Crossref]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1987)].

1979 (1)

R. J. Damburg and V. V. Kolosov, J. Phys. B 12, 2637 (1979).
[Crossref]

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[Crossref] [PubMed]

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1987)].

Aseyev, S. A.

S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, Phys. Rev. Lett. 91, 223902 (2003).
[Crossref]

Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[Crossref] [PubMed]

Balcou, Ph.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[Crossref] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[Crossref] [PubMed]

Brabec, T.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[Crossref] [PubMed]

Burnett, N. H.

Corkum, P.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

Corkum, P. B.

H. Niikura, F. Legare, R. Hasbani, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, Nature 421, 826 (2003).
[Crossref] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[Crossref] [PubMed]

P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, Opt. Lett. 19, 1870 (1994).
[Crossref]

P. B. Corkum, Phys. Rev. Lett. 71, 1995 (1993).
[Crossref]

Damburg, R. J.

R. J. Damburg and V. V. Kolosov, J. Phys. B 12, 2637 (1979).
[Crossref]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1987)].

Drescher, M.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

Frasinski, L. J.

S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, Phys. Rev. Lett. 91, 223902 (2003).
[Crossref]

Gürtler, A.

A. Gürtler, F. Robicheaux, M. J. J. Vrakking, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 063901 (2004).
[Crossref]

Hasbani, R.

H. Niikura, F. Legare, R. Hasbani, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, Nature 421, 826 (2003).
[Crossref] [PubMed]

Heinzmann, U.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

Hentschel, M.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

Ivanov, M. Y.

Ivanov, M. Yu.

H. Niikura, F. Legare, R. Hasbani, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, Nature 421, 826 (2003).
[Crossref] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[Crossref] [PubMed]

Kienberger, R.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

Kolosov, V. V.

R. J. Damburg and V. V. Kolosov, J. Phys. B 12, 2637 (1979).
[Crossref]

Krainov, V. P.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1987)].

Krausz, F.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

L’Huillier, A.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[Crossref] [PubMed]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Pergamon, Oxford, 1977), p. 1974.

Legare, F.

H. Niikura, F. Legare, R. Hasbani, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, Nature 421, 826 (2003).
[Crossref] [PubMed]

Lewenstein, M.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[Crossref] [PubMed]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Pergamon, Oxford, 1977), p. 1974.

Milosevic, N.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

Muller, H. G.

S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, Phys. Rev. Lett. 91, 223902 (2003).
[Crossref]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[Crossref] [PubMed]

Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[Crossref] [PubMed]

Ni, Y.

S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, Phys. Rev. Lett. 91, 223902 (2003).
[Crossref]

Niikura, H.

H. Niikura, F. Legare, R. Hasbani, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, Nature 421, 826 (2003).
[Crossref] [PubMed]

Noordam, L. D.

A. Gürtler, F. Robicheaux, M. J. J. Vrakking, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 063901 (2004).
[Crossref]

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[Crossref] [PubMed]

Reider, G. A.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

Robicheaux, F.

A. Gürtler, F. Robicheaux, M. J. J. Vrakking, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 063901 (2004).
[Crossref]

Spielmann, Ch.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[Crossref] [PubMed]

van der Zande, W. J.

A. Gürtler, F. Robicheaux, M. J. J. Vrakking, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 063901 (2004).
[Crossref]

Villeneuve, D. M.

H. Niikura, F. Legare, R. Hasbani, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, Nature 421, 826 (2003).
[Crossref] [PubMed]

Vrakking, M. J. J.

A. Gürtler, F. Robicheaux, M. J. J. Vrakking, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 063901 (2004).
[Crossref]

S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, Phys. Rev. Lett. 91, 223902 (2003).
[Crossref]

J. Phys. B (1)

R. J. Damburg and V. V. Kolosov, J. Phys. B 12, 2637 (1979).
[Crossref]

Nature (2)

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[Crossref] [PubMed]

H. Niikura, F. Legare, R. Hasbani, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, Nature 421, 826 (2003).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (1)

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

A. Gürtler, F. Robicheaux, M. J. J. Vrakking, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 063901 (2004).
[Crossref]

S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, Phys. Rev. Lett. 91, 223902 (2003).
[Crossref]

P. B. Corkum, Phys. Rev. Lett. 71, 1995 (1993).
[Crossref]

Science (1)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[Crossref] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1987)].

Other (2)

As the field is symmetric near t=0, one would also expect the ionization signal to be symmetric. However, as we keep the pulse energy constant, variations in the pulse parameters lead to high field values that deplete the population in the Rydberg states significantly, leading to the asymmetry observed in the figures.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Pergamon, Oxford, 1977), p. 1974.

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Figures (4)

Fig. 1
Fig. 1

RF pulse fields (bottom curves) and corresponding electron TOF measurements (top curves) for a 250-ns pulse duration and fundamental frequencies of 10 (left) and 20 (right) MHz. For (a) and (c), only the fundamental frequency is present, whereas for (b) and (d) an equally intense frequency contribution is added: (b) fundamental + second-harmonic frequency, (d) fundamental + incommensurate frequency.

Fig. 2
Fig. 2

Ionization yield versus time (top curves) for two different RF fields (bottom curves). Solid curves, RF field with only one frequency component f1=5.14 MHz, leading to ionization on every half-cycle. With only 9% (in energy) of second harmonic f2=10.28 MHz (dotted curves), electron emission occurs only once per fundamental cycle. The carrier phases of the two frequencies are null. Inset, duration of the main electron peak as a function of second-harmonic amplitude (N.B.: the total energy of the pulses was constant).

Fig. 3
Fig. 3

Duration of the most intense electron pulse as a function of the relative phase between the fundamental (5.14-MHz) and the second-harmonic (10.28-MHz) field oscillations (250-ns pulse duration, φ1=0). The energy of the pulses was kept constant for all values of the phase. The second-harmonic frequency contribution is 9% of the total energy. Inset, contour plot of the electron TOF as a function of the relative phase between the fundamental and second-harmonic field oscillations.

Fig. 4
Fig. 4

Electron TOF measurements for 250-ns long pulses (16 cycles) with different frequencies added to the fundamental frequency of 17.69 MHz. The contribution of the second frequency is 9% of the total energy.

Equations (1)

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Et=A exp-t/τ2cos2πf1t+φ1+α cos2πf2t+φ2,

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