Abstract

Rigorous quantum calculations of the femtosecond ionization of hydrogen atoms in air lead to highly anisotropic electron and ion angular (momentum) distributions. A quantum Monte-Carlo analysis of the subsequent many-body dynamics reveals two distinct relaxation steps, first to a nearly isotropic hot nonequilibrium and then to a quasi-equilibrium configuration. The collective isotropic plasma state is reached on a picosecond timescale well after the ultrashort ionizing pulse has passed.

© 2012 OSA

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  1. T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4, 822–832 (2010).
    [CrossRef]
  2. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
    [CrossRef]
  3. Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
    [CrossRef]
  4. D. G. Arbo, S. Yoshida, E. Persson, K. I. Dimitriou, and J. Burgdorfer, “Interference oscillations in the angular distribution of laser-ionized electrons near ionization threshold,” Phys. Rev. Lett. 96, 143003 (2006).
    [CrossRef] [PubMed]
  5. A. Rudenko, K. Zrost, C. D. Schroter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and J. Ullrich, “Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime,” J. Phys. B 37, L407–L413 (2004).
    [CrossRef]
  6. L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Butterworth-Heinemann, 1981)
  7. Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma filament,” Phys. Rev. E 83, 046408 (2011).
    [CrossRef]
  8. S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123–127 (2000).
    [CrossRef]
  9. Y. H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
    [CrossRef]
  10. P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xeon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
    [CrossRef]
  11. M. Wickenhauser, X. M. Tong, D. G. Arbo, J. Burgdoerfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
    [CrossRef]
  12. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
    [CrossRef] [PubMed]
  13. A. A. Silaev and N. V. Vvedenskii, “Residual-current excitation in plasmas produced by few-cycle laser pulses,” PRL 102, 115005 (2009).
    [CrossRef]
  14. see, e.g. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 5th ed. (World Scientific Publ., 2009), Chap. 8.
  15. C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulation (Springer-Verlag, 1989).
    [CrossRef]
  16. see, e.g., R. Brunetti, C. Jacoboni, A. Matulionis, and V. Dienys, “Effect of interparticle collisions on energy relaxation of carriers in semiconductors,” Physica B 134, 369–373 (1985) for self-scattering method for el.-el. Coulomb scattering.
    [CrossRef]

2011

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma filament,” Phys. Rev. E 83, 046408 (2011).
[CrossRef]

2010

Y. H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4, 822–832 (2010).
[CrossRef]

2009

A. A. Silaev and N. V. Vvedenskii, “Residual-current excitation in plasmas produced by few-cycle laser pulses,” PRL 102, 115005 (2009).
[CrossRef]

2007

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

2006

D. G. Arbo, S. Yoshida, E. Persson, K. I. Dimitriou, and J. Burgdorfer, “Interference oscillations in the angular distribution of laser-ionized electrons near ionization threshold,” Phys. Rev. Lett. 96, 143003 (2006).
[CrossRef] [PubMed]

M. Wickenhauser, X. M. Tong, D. G. Arbo, J. Burgdoerfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
[CrossRef]

2004

A. Rudenko, K. Zrost, C. D. Schroter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and J. Ullrich, “Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime,” J. Phys. B 37, L407–L413 (2004).
[CrossRef]

2001

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[CrossRef] [PubMed]

2000

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123–127 (2000).
[CrossRef]

1985

see, e.g., R. Brunetti, C. Jacoboni, A. Matulionis, and V. Dienys, “Effect of interparticle collisions on energy relaxation of carriers in semiconductors,” Physica B 134, 369–373 (1985) for self-scattering method for el.-el. Coulomb scattering.
[CrossRef]

1979

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xeon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Agostini, P.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xeon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Antonsen, T. M.

Y. H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

Arbo, D. G.

M. Wickenhauser, X. M. Tong, D. G. Arbo, J. Burgdoerfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
[CrossRef]

D. G. Arbo, S. Yoshida, E. Persson, K. I. Dimitriou, and J. Burgdorfer, “Interference oscillations in the angular distribution of laser-ionized electrons near ionization threshold,” Phys. Rev. Lett. 96, 143003 (2006).
[CrossRef] [PubMed]

Arpin, P.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4, 822–832 (2010).
[CrossRef]

Bakker, J. M.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Bauer, D.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Berden, G.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Brunetti, R.

see, e.g., R. Brunetti, C. Jacoboni, A. Matulionis, and V. Dienys, “Effect of interparticle collisions on energy relaxation of carriers in semiconductors,” Physica B 134, 369–373 (1985) for self-scattering method for el.-el. Coulomb scattering.
[CrossRef]

Burgdoerfer, J.

M. Wickenhauser, X. M. Tong, D. G. Arbo, J. Burgdoerfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
[CrossRef]

Burgdorfer, J.

D. G. Arbo, S. Yoshida, E. Persson, K. I. Dimitriou, and J. Burgdorfer, “Interference oscillations in the angular distribution of laser-ionized electrons near ionization threshold,” Phys. Rev. Lett. 96, 143003 (2006).
[CrossRef] [PubMed]

Cauchy, C.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Chen, J.

Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma filament,” Phys. Rev. E 83, 046408 (2011).
[CrossRef]

Chen, M.-C.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4, 822–832 (2010).
[CrossRef]

Chen, Y. H.

Y. H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

Couairon, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

de Jesus, V. L. B.

A. Rudenko, K. Zrost, C. D. Schroter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and J. Ullrich, “Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime,” J. Phys. B 37, L407–L413 (2004).
[CrossRef]

De Silvestri, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[CrossRef] [PubMed]

Dienys, V.

see, e.g., R. Brunetti, C. Jacoboni, A. Matulionis, and V. Dienys, “Effect of interparticle collisions on energy relaxation of carriers in semiconductors,” Physica B 134, 369–373 (1985) for self-scattering method for el.-el. Coulomb scattering.
[CrossRef]

Dimitriou, K. I.

D. G. Arbo, S. Yoshida, E. Persson, K. I. Dimitriou, and J. Burgdorfer, “Interference oscillations in the angular distribution of laser-ionized electrons near ionization threshold,” Phys. Rev. Lett. 96, 143003 (2006).
[CrossRef] [PubMed]

Fabre, F.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xeon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Feuerstein, B.

A. Rudenko, K. Zrost, C. D. Schroter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and J. Ullrich, “Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime,” J. Phys. B 37, L407–L413 (2004).
[CrossRef]

Franco, M.

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123–127 (2000).
[CrossRef]

Gijsbertsen, A.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Grasbon, F.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[CrossRef] [PubMed]

Haug, H.

see, e.g. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 5th ed. (World Scientific Publ., 2009), Chap. 8.

Huismans, Y.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Ivanov, M. Y.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Jacoboni, C.

see, e.g., R. Brunetti, C. Jacoboni, A. Matulionis, and V. Dienys, “Effect of interparticle collisions on energy relaxation of carriers in semiconductors,” Physica B 134, 369–373 (1985) for self-scattering method for el.-el. Coulomb scattering.
[CrossRef]

C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulation (Springer-Verlag, 1989).
[CrossRef]

Jungmann, J. H.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Kapteyn, H. C.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4, 822–832 (2010).
[CrossRef]

Koch, S. W.

see, e.g. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 5th ed. (World Scientific Publ., 2009), Chap. 8.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Butterworth-Heinemann, 1981)

Lepine, F.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Butterworth-Heinemann, 1981)

Lin, C. D.

M. Wickenhauser, X. M. Tong, D. G. Arbo, J. Burgdoerfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
[CrossRef]

Logman, P. S. W. M.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Lugli, P.

C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulation (Springer-Verlag, 1989).
[CrossRef]

Mainfray, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xeon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Marchenko, T.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Matulionis, A.

see, e.g., R. Brunetti, C. Jacoboni, A. Matulionis, and V. Dienys, “Effect of interparticle collisions on energy relaxation of carriers in semiconductors,” Physica B 134, 369–373 (1985) for self-scattering method for el.-el. Coulomb scattering.
[CrossRef]

Milchberg, H. M.

Y. H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

Moshammer, R.

A. Rudenko, K. Zrost, C. D. Schroter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and J. Ullrich, “Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime,” J. Phys. B 37, L407–L413 (2004).
[CrossRef]

Muller, H. G.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Murnane, M. M.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4, 822–832 (2010).
[CrossRef]

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123–127 (2000).
[CrossRef]

Nisoli, M.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[CrossRef] [PubMed]

Paulus, G. G.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[CrossRef] [PubMed]

Persson, E.

D. G. Arbo, S. Yoshida, E. Persson, K. I. Dimitriou, and J. Burgdorfer, “Interference oscillations in the angular distribution of laser-ionized electrons near ionization threshold,” Phys. Rev. Lett. 96, 143003 (2006).
[CrossRef] [PubMed]

Petite, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xeon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Popmintchev, T.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4, 822–832 (2010).
[CrossRef]

Popruzhenko, S. V.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Prade, B.

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123–127 (2000).
[CrossRef]

Priori, E.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[CrossRef] [PubMed]

Rahman, N. K.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xeon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Redlich, B.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Rouzee, A.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Rudenko, A.

A. Rudenko, K. Zrost, C. D. Schroter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and J. Ullrich, “Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime,” J. Phys. B 37, L407–L413 (2004).
[CrossRef]

Rudolph, W.

Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma filament,” Phys. Rev. E 83, 046408 (2011).
[CrossRef]

Schafer, K. J.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Schroter, C. D.

A. Rudenko, K. Zrost, C. D. Schroter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and J. Ullrich, “Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime,” J. Phys. B 37, L407–L413 (2004).
[CrossRef]

Silaev, A. A.

A. A. Silaev and N. V. Vvedenskii, “Residual-current excitation in plasmas produced by few-cycle laser pulses,” PRL 102, 115005 (2009).
[CrossRef]

Smirnova, O.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Smolkowska, A. S.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Spanner, M.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Stagira, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[CrossRef] [PubMed]

Sun, Z.

Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma filament,” Phys. Rev. E 83, 046408 (2011).
[CrossRef]

Tong, X. M.

M. Wickenhauser, X. M. Tong, D. G. Arbo, J. Burgdoerfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
[CrossRef]

Tzortzakis, S.

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123–127 (2000).
[CrossRef]

Ullrich, J.

A. Rudenko, K. Zrost, C. D. Schroter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and J. Ullrich, “Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime,” J. Phys. B 37, L407–L413 (2004).
[CrossRef]

van der Meer, A. F. G.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Varma, S.

Y. H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

Vermin, W.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Villoresi, P.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[CrossRef] [PubMed]

Vrakking, M. J. J.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Vvedenskii, N. V.

A. A. Silaev and N. V. Vvedenskii, “Residual-current excitation in plasmas produced by few-cycle laser pulses,” PRL 102, 115005 (2009).
[CrossRef]

Walther, H.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[CrossRef] [PubMed]

Wickenhauser, M.

M. Wickenhauser, X. M. Tong, D. G. Arbo, J. Burgdoerfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
[CrossRef]

Yoshida, S.

D. G. Arbo, S. Yoshida, E. Persson, K. I. Dimitriou, and J. Burgdorfer, “Interference oscillations in the angular distribution of laser-ionized electrons near ionization threshold,” Phys. Rev. Lett. 96, 143003 (2006).
[CrossRef] [PubMed]

Zamith, S.

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Zrost, K.

A. Rudenko, K. Zrost, C. D. Schroter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and J. Ullrich, “Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime,” J. Phys. B 37, L407–L413 (2004).
[CrossRef]

J. Phys. B

A. Rudenko, K. Zrost, C. D. Schroter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and J. Ullrich, “Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime,” J. Phys. B 37, L407–L413 (2004).
[CrossRef]

Nat. Photonics

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4, 822–832 (2010).
[CrossRef]

Nature

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[CrossRef] [PubMed]

Opt. Commun.

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123–127 (2000).
[CrossRef]

Phys. Rep.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

Phys. Rev. A

M. Wickenhauser, X. M. Tong, D. G. Arbo, J. Burgdoerfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
[CrossRef]

Phys. Rev. E

Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma filament,” Phys. Rev. E 83, 046408 (2011).
[CrossRef]

Phys. Rev. Lett.

D. G. Arbo, S. Yoshida, E. Persson, K. I. Dimitriou, and J. Burgdorfer, “Interference oscillations in the angular distribution of laser-ionized electrons near ionization threshold,” Phys. Rev. Lett. 96, 143003 (2006).
[CrossRef] [PubMed]

Y. H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xeon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Physica B

see, e.g., R. Brunetti, C. Jacoboni, A. Matulionis, and V. Dienys, “Effect of interparticle collisions on energy relaxation of carriers in semiconductors,” Physica B 134, 369–373 (1985) for self-scattering method for el.-el. Coulomb scattering.
[CrossRef]

PRL

A. A. Silaev and N. V. Vvedenskii, “Residual-current excitation in plasmas produced by few-cycle laser pulses,” PRL 102, 115005 (2009).
[CrossRef]

Science

Y. Huismans, A. Rouzee, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lepine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331, 61–64 (2011).
[CrossRef]

Other

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Butterworth-Heinemann, 1981)

see, e.g. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 5th ed. (World Scientific Publ., 2009), Chap. 8.

C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulation (Springer-Verlag, 1989).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Relaxation of an anisotropic nonequilibrium electron distribution created by ionizing hydrogen atoms with a 400 nm 3-cycle pulse of intensity I = 1 × 1014W/cm2. Above, H(k,θ) for different times in units of 1/fpl (Ne) (a) t = 0, (b) t = 0.31, (c) t = 1.04 and (d) t = 6.25. Here, kz = k cos(θ) and k ρ = k sin ( θ ) = ( k x 2 + k y 2 ) 1 / 2. Below, in (e) the corresponding θ-angle integrated (k). The yellow area shows the final Fermi Dirac distribution with T = 19797 K and Ē = 2.559 eV for (e). The total electron density is Ne = 2.155 × 1023/m3 which corresponds to an inverse 3D plasma frequency 1/fpl (Ne) = 0.240 ps.

Fig. 2
Fig. 2

Relaxation of an anisotropic nonequilibrium electron distribution created by ionizing hydrogen atoms with a 400 nm 3-cycle pulse of intensity I = 5 × 1013W/cm2. Above, H(k,θ) for different times in units of 1/fpl (Ne) (a) t = 0, (b) t = 0.31, (c) t = 1.04, (d) t = 6.27. Below, in (e) the corresponding θ-angle integrated (k). The yellow area shows the final Fermi Dirac distribution with T = 14273 K and Ē = 1.845 eV. The total electron density in (a)–(e) is Ne = 2.402 × 1022/m3 which corresponds to an inverse 3D plasma frequency 1/fpl (Ne) = 0.718 ps.

Fig. 3
Fig. 3

Relaxation of an anisotropic nonequilibrium electron distribution created by ionizing hydrogen atoms with a 400 nm 6-cycle pulse of intensity I = 5 × 1013W/cm2. Above, H(k,θ) for different times (a) t = 0/fpl, (b) t = 0.25/fpl, (c) t = 1/fpl, (d) t = 5/fpl. Below, in (e) (k) for the same times. The yellow area shows the final Fermi Dirac distribution (T = 14283 K, Ē = 1.846 eV). The total electron density is Ne = 7.743 × 1022/m3 corresponding to an inverse 3D plasma frequency of approximately 1/fpl (Ne) = 0.400 ps.

Fig. 4
Fig. 4

Relaxation times calculated from H(k,θ) (a), the calculated anisotropy (b) and the average kz momentum (c) for the ionization conditions: 400 nm pulse with 3 cycles and I = 5 × 1013W/cm2 (solid, red) as well as I = 1 × 1014W/cm2 (dashed dotted, black) and a 400 nm pulse 6 cycles pulse of intensity 5 × 1013W/cm2 (dotted, blue). The time is given in units of 1/fpl, i.e. 0.718 ps (red), 0.240 ps (black) and 0.400 ps (blue). The short-time relaxation dynamics happens in the regime below 1/fpl. The gray lines are exponential fits to the long-time dynamics.

Equations (8)

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

[ t + h ¯ k m e r 1 h ¯ ( V ) k ] f W e ( r , k , t ) = t f W e ( r , k , t ) | collision + t f W e ( r , k , t ) | ionization + t f W e ( r , k , t ) | recombination .
i h ¯ t Ψ ( ρ , z ; t ) = [ p 2 2 m e e 2 4 π ɛ 0 r + e E ( t ) z ] Ψ ( ρ , z ; t )
E ( t ) = E 0 sin 2 ( π t T ) sin ( ω t + χ ) .
t f k e | e λ collision = 2 π h ¯ p , q V | q | 2 ( 1 f k e ) ( 1 f p λ ) f k q e f p + q λ δ ( Δ E k , p , q e , λ ) 2 π h ¯ p , q V | q | 2 f k e f p λ ( 1 f k q e ) ( 1 f p + q λ ) δ ( Δ E k , p , q e , λ ) λ { e , i } , Δ E k , p , q e , λ = h ¯ 2 | k | 2 h ¯ 2 | k q | 2 2 m e + h ¯ 2 | p | 2 h ¯ 2 | p + q | 2 2 m λ
H ( k , θ ) = k 2 4 π 2 f ( k , θ )
H ¯ ( k ) = 1 2 0 π sin ( θ ) H ( k , θ ) d θ .
r ( t ) = d k sin ( θ ) d θ | H ( k , θ , t ) H ( k , θ , equilibrium ) | d k sin ( θ ) d θ | H ( k , θ , t = 0 ) H ( k , θ , equilibrium ) |
i ( t ) = d k sin ( θ ) d θ | H ( k , θ , t ) H ¯ ( k , t ) | d k sin ( θ ) d θ | H ( k , θ , t = 0 ) H ( k , t = 0 ) |

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