Abstract

A nonlinear interferometry scheme is described theoretically to induce and resolve electron wavefunction beating on time scales shorter than the optical cycle of the time-delayed pump and probe pulses. By employing two moderately intense few-cycle laser fields with a stable carrier-envelope phase, a large range of the entire electronic level structure of a quantum system can be retrieved. In contrast to single-photon excitation schemes, the retrieved electronic states include levels that are both dipole-and non-dipole-accessible from the ground electronic state. The results show that strong-field interferometry can reveal both high-resolution and broad-band spectral information at the same time with important consequences for quantum-beat spectroscopy on attosecond time scales.

© 2010 Optical Society of America

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  1. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
    [CrossRef] [PubMed]
  2. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432, 605-608 (2004).
    [CrossRef] [PubMed]
  3. P. B. Corkum, and F. Krausz, "Attosecond science," Nat. Phys. 3, 381-387 (2007).
    [CrossRef]
  4. J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
    [CrossRef] [PubMed]
  5. L. R. Khundkar, and A. H. Zewail, "Ultrafast molecular reaction dynamics in real-time - progress over a decade," Annu. Rev. Phys. Chem. 41, 15-60 (1990).
    [CrossRef]
  6. N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
    [CrossRef]
  7. B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
    [CrossRef] [PubMed]
  8. M. Winter, R. Schmidt, and U. Thumm, "Multidimensional quantum-beat spectroscopy: Towards the complete temporal and spatial resolution of the nuclear dynamics in small molecules," Phys. Rev. A 80, 031401 (2009).
    [CrossRef]
  9. R. R. Jones, C. S. Raman, D. W. Schumacher, and P. H. Bucksbaum, "Ramsey interference in strongly driven Rydberg systems," Phys. Rev. Lett. 71, 2575-2578 (1993).
    [CrossRef] [PubMed]
  10. M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
    [CrossRef] [PubMed]
  11. A. Palacios, T. N. Rescigno, and C. W. McCurdy, "Two-electron time-delay interference in atomic double ionization by attosecond pulses," Phys. Rev. Lett. 103, 253001 (2009).
    [CrossRef]
  12. T. Nubbemeyer, K. Gorling, A. Saenz, and U. Eichmann, "andW. Sandner, "Strong-field tunneling without ionization," Phys. Rev. Lett. 101, 233001 (2008).
    [CrossRef] [PubMed]
  13. U. Eichmann, T. Nubbemeyer, H. Rottke, and W. Sandner, "Acceleration of neutral atoms in strong short-pulse laser fields," Nature 461, 1261-1264 (2009).
    [CrossRef] [PubMed]
  14. J. Javanainen, J. H. Eberly, and Q. C. Su, "Numerical simulations of multiphoton ionization and above-threshold electron-spectra," Phys. Rev. A 38, 3430-3446 (1988).
    [CrossRef] [PubMed]
  15. J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129-160 (1976).
    [CrossRef]
  16. M. D. Feit, J. A. Fleck, and A. Steiger, "Solution of the Schrödinger-equation by a spectral method," J. Comput. Phys. 47, 412-433 (1982).
    [CrossRef]
  17. T. Pfeifer, D. Walter, G. Gerber, M. Y. Emelin, M. Y. Ryabikin, M. D. Chernobrovtseva, and A. M. Sergeev, "Transient enhancement of high-harmonic generation in expanding molecules," Phys. Rev. A 70, 013805 (2004).
    [CrossRef]

2010 (1)

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

2009 (3)

M. Winter, R. Schmidt, and U. Thumm, "Multidimensional quantum-beat spectroscopy: Towards the complete temporal and spatial resolution of the nuclear dynamics in small molecules," Phys. Rev. A 80, 031401 (2009).
[CrossRef]

A. Palacios, T. N. Rescigno, and C. W. McCurdy, "Two-electron time-delay interference in atomic double ionization by attosecond pulses," Phys. Rev. Lett. 103, 253001 (2009).
[CrossRef]

U. Eichmann, T. Nubbemeyer, H. Rottke, and W. Sandner, "Acceleration of neutral atoms in strong short-pulse laser fields," Nature 461, 1261-1264 (2009).
[CrossRef] [PubMed]

2008 (2)

T. Nubbemeyer, K. Gorling, A. Saenz, and U. Eichmann, "andW. Sandner, "Strong-field tunneling without ionization," Phys. Rev. Lett. 101, 233001 (2008).
[CrossRef] [PubMed]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

2007 (2)

P. B. Corkum, and F. Krausz, "Attosecond science," Nat. Phys. 3, 381-387 (2007).
[CrossRef]

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
[CrossRef] [PubMed]

2004 (2)

T. Pfeifer, D. Walter, G. Gerber, M. Y. Emelin, M. Y. Ryabikin, M. D. Chernobrovtseva, and A. M. Sergeev, "Transient enhancement of high-harmonic generation in expanding molecules," Phys. Rev. A 70, 013805 (2004).
[CrossRef]

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432, 605-608 (2004).
[CrossRef] [PubMed]

2002 (1)

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

1993 (1)

R. R. Jones, C. S. Raman, D. W. Schumacher, and P. H. Bucksbaum, "Ramsey interference in strongly driven Rydberg systems," Phys. Rev. Lett. 71, 2575-2578 (1993).
[CrossRef] [PubMed]

1991 (1)

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

1990 (1)

L. R. Khundkar, and A. H. Zewail, "Ultrafast molecular reaction dynamics in real-time - progress over a decade," Annu. Rev. Phys. Chem. 41, 15-60 (1990).
[CrossRef]

1988 (1)

J. Javanainen, J. H. Eberly, and Q. C. Su, "Numerical simulations of multiphoton ionization and above-threshold electron-spectra," Phys. Rev. A 38, 3430-3446 (1988).
[CrossRef] [PubMed]

1982 (1)

M. D. Feit, J. A. Fleck, and A. Steiger, "Solution of the Schrödinger-equation by a spectral method," J. Comput. Phys. 47, 412-433 (1982).
[CrossRef]

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129-160 (1976).
[CrossRef]

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Assion, A.

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Baumert, T.

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Benedetti, E.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Bouchene, M. A.

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Bucksbaum, P. H.

R. R. Jones, C. S. Raman, D. W. Schumacher, and P. H. Bucksbaum, "Ramsey interference in strongly driven Rydberg systems," Phys. Rev. Lett. 71, 2575-2578 (1993).
[CrossRef] [PubMed]

Carlson, R. J.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

Chernobrovtseva, M. D.

T. Pfeifer, D. Walter, G. Gerber, M. Y. Emelin, M. Y. Ryabikin, M. D. Chernobrovtseva, and A. M. Sergeev, "Transient enhancement of high-harmonic generation in expanding molecules," Phys. Rev. A 70, 013805 (2004).
[CrossRef]

Cina, J. A.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

Corkum, P. B.

P. B. Corkum, and F. Krausz, "Attosecond science," Nat. Phys. 3, 381-387 (2007).
[CrossRef]

Du, M.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

Eberly, J. H.

J. Javanainen, J. H. Eberly, and Q. C. Su, "Numerical simulations of multiphoton ionization and above-threshold electron-spectra," Phys. Rev. A 38, 3430-3446 (1988).
[CrossRef] [PubMed]

Eichmann, U.

U. Eichmann, T. Nubbemeyer, H. Rottke, and W. Sandner, "Acceleration of neutral atoms in strong short-pulse laser fields," Nature 461, 1261-1264 (2009).
[CrossRef] [PubMed]

T. Nubbemeyer, K. Gorling, A. Saenz, and U. Eichmann, "andW. Sandner, "Strong-field tunneling without ionization," Phys. Rev. Lett. 101, 233001 (2008).
[CrossRef] [PubMed]

Emelin, M. Y.

T. Pfeifer, D. Walter, G. Gerber, M. Y. Emelin, M. Y. Ryabikin, M. D. Chernobrovtseva, and A. M. Sergeev, "Transient enhancement of high-harmonic generation in expanding molecules," Phys. Rev. A 70, 013805 (2004).
[CrossRef]

Ergler, T.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
[CrossRef] [PubMed]

Feit, M. D.

M. D. Feit, J. A. Fleck, and A. Steiger, "Solution of the Schrödinger-equation by a spectral method," J. Comput. Phys. 47, 412-433 (1982).
[CrossRef]

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129-160 (1976).
[CrossRef]

Ferrari, F.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Feuerstein, B.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
[CrossRef] [PubMed]

Fleck, J. A.

M. D. Feit, J. A. Fleck, and A. Steiger, "Solution of the Schrödinger-equation by a spectral method," J. Comput. Phys. 47, 412-433 (1982).
[CrossRef]

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129-160 (1976).
[CrossRef]

Fleming, G. R.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

Flettner, A.

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Gagnon, J.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Gerber, G.

T. Pfeifer, D. Walter, G. Gerber, M. Y. Emelin, M. Y. Ryabikin, M. D. Chernobrovtseva, and A. M. Sergeev, "Transient enhancement of high-harmonic generation in expanding molecules," Phys. Rev. A 70, 013805 (2004).
[CrossRef]

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Ghafur, O.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Girard, B.

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Gorling, K.

T. Nubbemeyer, K. Gorling, A. Saenz, and U. Eichmann, "andW. Sandner, "Strong-field tunneling without ionization," Phys. Rev. Lett. 101, 233001 (2008).
[CrossRef] [PubMed]

Goulielmakis, E.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Gullikson, E. M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Hofstetter, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Javanainen, J.

J. Javanainen, J. H. Eberly, and Q. C. Su, "Numerical simulations of multiphoton ionization and above-threshold electron-spectra," Phys. Rev. A 38, 3430-3446 (1988).
[CrossRef] [PubMed]

Johnsson, P.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Jones, R. R.

R. R. Jones, C. S. Raman, D. W. Schumacher, and P. H. Bucksbaum, "Ramsey interference in strongly driven Rydberg systems," Phys. Rev. Lett. 71, 2575-2578 (1993).
[CrossRef] [PubMed]

Kanai, T.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432, 605-608 (2004).
[CrossRef] [PubMed]

Kelkensberg, F.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Khundkar, L. R.

L. R. Khundkar, and A. H. Zewail, "Ultrafast molecular reaction dynamics in real-time - progress over a decade," Annu. Rev. Phys. Chem. 41, 15-60 (1990).
[CrossRef]

Kienberger, R.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Kleineberg, U.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Kling, M. F.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Klunder, K.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Kosuge, A.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432, 605-608 (2004).
[CrossRef] [PubMed]

Krausz, F.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

P. B. Corkum, and F. Krausz, "Attosecond science," Nat. Phys. 3, 381-387 (2007).
[CrossRef]

L’Huillier, A.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Lepine, F.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Liese, D.

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Matro, A.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

Mauritsson, J.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

McCurdy, C. W.

A. Palacios, T. N. Rescigno, and C. W. McCurdy, "Two-electron time-delay interference in atomic double ionization by attosecond pulses," Phys. Rev. Lett. 103, 253001 (2009).
[CrossRef]

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129-160 (1976).
[CrossRef]

Moshammer, R.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
[CrossRef] [PubMed]

Niederhausen, T.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
[CrossRef] [PubMed]

Nisoli, M.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Nubbemeyer, T.

U. Eichmann, T. Nubbemeyer, H. Rottke, and W. Sandner, "Acceleration of neutral atoms in strong short-pulse laser fields," Nature 461, 1261-1264 (2009).
[CrossRef] [PubMed]

T. Nubbemeyer, K. Gorling, A. Saenz, and U. Eichmann, "andW. Sandner, "Strong-field tunneling without ionization," Phys. Rev. Lett. 101, 233001 (2008).
[CrossRef] [PubMed]

Palacios, A.

A. Palacios, T. N. Rescigno, and C. W. McCurdy, "Two-electron time-delay interference in atomic double ionization by attosecond pulses," Phys. Rev. Lett. 103, 253001 (2009).
[CrossRef]

Pfeifer, T.

T. Pfeifer, D. Walter, G. Gerber, M. Y. Emelin, M. Y. Ryabikin, M. D. Chernobrovtseva, and A. M. Sergeev, "Transient enhancement of high-harmonic generation in expanding molecules," Phys. Rev. A 70, 013805 (2004).
[CrossRef]

Raman, C. S.

R. R. Jones, C. S. Raman, D. W. Schumacher, and P. H. Bucksbaum, "Ramsey interference in strongly driven Rydberg systems," Phys. Rev. Lett. 71, 2575-2578 (1993).
[CrossRef] [PubMed]

Remetter, T.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Rescigno, T. N.

A. Palacios, T. N. Rescigno, and C. W. McCurdy, "Two-electron time-delay interference in atomic double ionization by attosecond pulses," Phys. Rev. Lett. 103, 253001 (2009).
[CrossRef]

Rice, S. A.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

Romerorochin, V.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

Rottke, H.

U. Eichmann, T. Nubbemeyer, H. Rottke, and W. Sandner, "Acceleration of neutral atoms in strong short-pulse laser fields," Nature 461, 1261-1264 (2009).
[CrossRef] [PubMed]

Rudenko, A.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
[CrossRef] [PubMed]

Ruggiero, A. J.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

Ryabikin, M. Y.

T. Pfeifer, D. Walter, G. Gerber, M. Y. Emelin, M. Y. Ryabikin, M. D. Chernobrovtseva, and A. M. Sergeev, "Transient enhancement of high-harmonic generation in expanding molecules," Phys. Rev. A 70, 013805 (2004).
[CrossRef]

Saenz, A.

T. Nubbemeyer, K. Gorling, A. Saenz, and U. Eichmann, "andW. Sandner, "Strong-field tunneling without ionization," Phys. Rev. Lett. 101, 233001 (2008).
[CrossRef] [PubMed]

Sandner, W.

U. Eichmann, T. Nubbemeyer, H. Rottke, and W. Sandner, "Acceleration of neutral atoms in strong short-pulse laser fields," Nature 461, 1261-1264 (2009).
[CrossRef] [PubMed]

Sansone, G.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Sarpe-Tudoran, C.

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Schafer, K. J.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Scherer, N. F.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

Schmidt, R.

M. Winter, R. Schmidt, and U. Thumm, "Multidimensional quantum-beat spectroscopy: Towards the complete temporal and spatial resolution of the nuclear dynamics in small molecules," Phys. Rev. A 80, 031401 (2009).
[CrossRef]

Schroter, C. D.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
[CrossRef] [PubMed]

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Schumacher, D. W.

R. R. Jones, C. S. Raman, D. W. Schumacher, and P. H. Bucksbaum, "Ramsey interference in strongly driven Rydberg systems," Phys. Rev. Lett. 71, 2575-2578 (1993).
[CrossRef] [PubMed]

Sekikawa, T.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432, 605-608 (2004).
[CrossRef] [PubMed]

Sergeev, A. M.

T. Pfeifer, D. Walter, G. Gerber, M. Y. Emelin, M. Y. Ryabikin, M. D. Chernobrovtseva, and A. M. Sergeev, "Transient enhancement of high-harmonic generation in expanding molecules," Phys. Rev. A 70, 013805 (2004).
[CrossRef]

Siu, W.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Steiger, A.

M. D. Feit, J. A. Fleck, and A. Steiger, "Solution of the Schrödinger-equation by a spectral method," J. Comput. Phys. 47, 412-433 (1982).
[CrossRef]

Su, Q. C.

J. Javanainen, J. H. Eberly, and Q. C. Su, "Numerical simulations of multiphoton ionization and above-threshold electron-spectra," Phys. Rev. A 38, 3430-3446 (1988).
[CrossRef] [PubMed]

Swoboda, M.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Thumm, U.

M. Winter, R. Schmidt, and U. Thumm, "Multidimensional quantum-beat spectroscopy: Towards the complete temporal and spatial resolution of the nuclear dynamics in small molecules," Phys. Rev. A 80, 031401 (2009).
[CrossRef]

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
[CrossRef] [PubMed]

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Ullrich, J.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
[CrossRef] [PubMed]

Uphues, T.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Vrakking, M. J. J.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Walter, D.

T. Pfeifer, D. Walter, G. Gerber, M. Y. Emelin, M. Y. Ryabikin, M. D. Chernobrovtseva, and A. M. Sergeev, "Transient enhancement of high-harmonic generation in expanding molecules," Phys. Rev. A 70, 013805 (2004).
[CrossRef]

Watanabe, S.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432, 605-608 (2004).
[CrossRef] [PubMed]

Weichmann, U.

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Winter, M.

M. Winter, R. Schmidt, and U. Thumm, "Multidimensional quantum-beat spectroscopy: Towards the complete temporal and spatial resolution of the nuclear dynamics in small molecules," Phys. Rev. A 80, 031401 (2009).
[CrossRef]

Wollenhaupt, M.

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Yakovlev, V. S.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Zamith, S.

M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, "Interferences of ultrashort free electron wave packets," Phys. Rev. Lett. 89, 173001 (2002).
[CrossRef] [PubMed]

Zewail, A. H.

L. R. Khundkar, and A. H. Zewail, "Ultrafast molecular reaction dynamics in real-time - progress over a decade," Annu. Rev. Phys. Chem. 41, 15-60 (1990).
[CrossRef]

Zherebtsov, S.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Znakovskaya, I.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klunder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, "Attosecond electron spectroscopy using a novel interferometric pump-probe technique," Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef] [PubMed]

Zrost, K.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schroter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, "Complete characterization of molecular dynamics in ultrashort laser fields," Phys. Rev. Lett. 99, 153002 (2007).
[CrossRef] [PubMed]

Annu. Rev. Phys. Chem. (1)

L. R. Khundkar, and A. H. Zewail, "Ultrafast molecular reaction dynamics in real-time - progress over a decade," Annu. Rev. Phys. Chem. 41, 15-60 (1990).
[CrossRef]

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129-160 (1976).
[CrossRef]

J. Chem. Phys. (1)

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romerorochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry - time resolved molecular-spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991).
[CrossRef]

J. Comput. Phys. (1)

M. D. Feit, J. A. Fleck, and A. Steiger, "Solution of the Schrödinger-equation by a spectral method," J. Comput. Phys. 47, 412-433 (1982).
[CrossRef]

Nat. Phys. (1)

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Figures (4)

Fig. 1
Fig. 1

Photoelectron momentum spectra (a) for one single pulse, (b) and (c) for two identical pulses at two different time delays τ (solid lines). In (b) and (c), the rescaled (times 4) single-pulse spectrum of (a) is also shown (dashed line). A vertical dotted line at an electron momentum pe = 0.415 is drawn to highlight the time-delay-dependent modulation.

Fig. 2
Fig. 2

Delay-time dependent photoelectron spectrum (a) at the selected photoelectron momentum pe = 0.415 (dotted line in Fig. 1), (b) for a broad range of photoelectron momenta. The single-pulse spectrum from Fig. 1a is additionally shown in (c). Attosecond time-scale beatings are clearly observable as a function of time delay. Note the momentum-dependent visibility of the modulation in (b) corresponding to the peaks and dips of the single-pulse photoelectron spectrum (c).

Fig. 3
Fig. 3

Beating frequencies of electronic bound and continuum states after Fourier transform of the data in Fig. 2(b): (a) Lineout at momentum pe = 0.415, (b) for all photoelectron momenta. Each Fourier-transformed spectrum is normalized to its zero-frequency component. The visible horizontal lines are due to noise enhanced by this normalization procedure and contain no physical meaning. (c) The single-pulse photoelectron spectrum from Fig. 1(a). (d) Momentum-integrated frequency spectrum (see text for details).

Fig. 4
Fig. 4

(a) Momentum-integrated frequency spectrum of the electron beating signal (from Fig. 3), (dashed red line: laser pulse spectrum). Spectrum of the electron position (b) and position-squared (c) expectation value of the electronic wavefunction after interaction with the pump pulse, corresponding to the dipole- and quadrupole-active transitions, respectively. The agreement of the spectral positions of the wavepacket beatings in (b) and (c) with the observable data from (a) is excellent.

Equations (7)

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| Ψ ( t ) = Σ n b n e i E n t | ψ n + k d 3 k c ( k ) e i 2 k 2 t | k ,
| Ψ ˜ c ( t ) = k d 3 k | k k | L ^ pr | Ψ ( τ ) e i 2 k 2 ( t τ ) = k d 3 k c ˜ ( k ) e i 2 k 2 ( t τ ) | k
c ˜ ( k ) = Σ n c n ( k ) e i E n τ + c ( k ) e i 2 k 2 τ
c n ( k ) = L pr k n b n
c ( k ) = c ( k ) e i 2 t 1 t 2 A ( t ) 2 dt ,
S ( k ) = | c ˜ ( k ) | 2 Σ n | c n ( k ) | 2 + | c ( k ) | 2 + [ n , m < n c n ( k ) c m * ( k ) e i ( E n E m ) τ + n c n ( k ) c * ( k ) e i ( E n 1 2 k 2 ) τ + c . c . ] .
H ^ = ( p ^ + A ( t ) ) 2 2 1 x ^ 2 + a 2

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