Abstract

Using numerical solutions of the time-dependent Schrödinger equation for a hydrogen and a helium atom in a linearly polarized, few-cycle laser field, we calculate the photoelectron left–right asymmetry measured by two opposing detectors placed along the laser polarization vector, with the laser focus in the center. We find a simple dependence of this asymmetry on carrier-envelope (CE) phase ϕ for laser intensities slightly below the tunneling regime, which may allow us to measure (or to calibrate) and to stabilize the CE phase. In particular, we suggest that the condition of zero asymmetry for few-cycle pulses may be useful for both these goals.

© 2004 Optical Society of America

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References

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  1. T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
    [CrossRef]
  2. V. S. Yakovlev, P. Dombi, G. Tempea, C. Lemell, J. Burgdörfer, T. Udem, and A. Apolonski, Appl. Phys. B 76, 329 (2003).
    [CrossRef]
  3. S. Chelkowski and A. D. Bandrauk, Phys. Rev. A 65, 061802 (2002).
    [CrossRef]
  4. S. Chelkowski, N. H. Shon, and A. D. Bandrauk, Laser Phys. 13, 871 (2003).
  5. D. B. Milosevic, G. G. Paulus, and W. Becker, Opt. Express 11, 1418 (2003), http://www.opticsexpress.org .
    [CrossRef]
  6. G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
    [CrossRef]
  7. A. Guertler, F. Robicheaux, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 033002 (2004).
    [CrossRef]
  8. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
    [CrossRef] [PubMed]
  9. A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
    [CrossRef]
  10. T. M. Fortier, P. A. Ross, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
    [CrossRef]
  11. P. L. Devries, J. Opt. Soc. Am. B 7, 517 (1990).
    [CrossRef]
  12. S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A (to be published).

2004 (3)

A. Guertler, F. Robicheaux, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 033002 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

T. M. Fortier, P. A. Ross, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef]

2003 (4)

V. S. Yakovlev, P. Dombi, G. Tempea, C. Lemell, J. Burgdörfer, T. Udem, and A. Apolonski, Appl. Phys. B 76, 329 (2003).
[CrossRef]

S. Chelkowski, N. H. Shon, and A. D. Bandrauk, Laser Phys. 13, 871 (2003).

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

D. B. Milosevic, G. G. Paulus, and W. Becker, Opt. Express 11, 1418 (2003), http://www.opticsexpress.org .
[CrossRef]

2002 (1)

S. Chelkowski and A. D. Bandrauk, Phys. Rev. A 65, 061802 (2002).
[CrossRef]

2001 (1)

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

2000 (1)

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

1990 (1)

Apolonski, A.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

V. S. Yakovlev, P. Dombi, G. Tempea, C. Lemell, J. Burgdörfer, T. Udem, and A. Apolonski, Appl. Phys. B 76, 329 (2003).
[CrossRef]

S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A (to be published).

Baltuska, A.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Bandrauk, A. D.

S. Chelkowski, N. H. Shon, and A. D. Bandrauk, Laser Phys. 13, 871 (2003).

S. Chelkowski and A. D. Bandrauk, Phys. Rev. A 65, 061802 (2002).
[CrossRef]

S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A (to be published).

Becker, W.

Bhat, R. D. R.

T. M. Fortier, P. A. Ross, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef]

Brabec, T.

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Burgdörfer, J.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

V. S. Yakovlev, P. Dombi, G. Tempea, C. Lemell, J. Burgdörfer, T. Udem, and A. Apolonski, Appl. Phys. B 76, 329 (2003).
[CrossRef]

Chelkowski, S.

S. Chelkowski, N. H. Shon, and A. D. Bandrauk, Laser Phys. 13, 871 (2003).

S. Chelkowski and A. D. Bandrauk, Phys. Rev. A 65, 061802 (2002).
[CrossRef]

S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A (to be published).

Cundiff, S. T.

T. M. Fortier, P. A. Ross, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef]

DeSilvestri, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Devries, P. L.

Dombi, P.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

V. S. Yakovlev, P. Dombi, G. Tempea, C. Lemell, J. Burgdörfer, T. Udem, and A. Apolonski, Appl. Phys. B 76, 329 (2003).
[CrossRef]

Fortier, T. M.

T. M. Fortier, P. A. Ross, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef]

Goulielmakis, E.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Grasbon, F.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Guertler, A.

A. Guertler, F. Robicheaux, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 033002 (2004).
[CrossRef]

Hänsch, T. W.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

Holzwart, R.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

Jones, D. J.

T. M. Fortier, P. A. Ross, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef]

Kakehata, M.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

Krausz, F.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Lemell, C.

V. S. Yakovlev, P. Dombi, G. Tempea, C. Lemell, J. Burgdörfer, T. Udem, and A. Apolonski, Appl. Phys. B 76, 329 (2003).
[CrossRef]

Lemell, Ch.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

Lezius, M.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Lindner, F.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Milosevic, D. B.

Nisoli, M.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Noordam, L. D.

A. Guertler, F. Robicheaux, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 033002 (2004).
[CrossRef]

Paulus, G. G.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

D. B. Milosevic, G. G. Paulus, and W. Becker, Opt. Express 11, 1418 (2003), http://www.opticsexpress.org .
[CrossRef]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Priori, E.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Robicheaux, F.

A. Guertler, F. Robicheaux, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 033002 (2004).
[CrossRef]

Ross, P. A.

T. M. Fortier, P. A. Ross, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef]

Shon, N. H.

S. Chelkowski, N. H. Shon, and A. D. Bandrauk, Laser Phys. 13, 871 (2003).

Sipe, J. E.

T. M. Fortier, P. A. Ross, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef]

Stagira, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Tempea, G.

V. S. Yakovlev, P. Dombi, G. Tempea, C. Lemell, J. Burgdörfer, T. Udem, and A. Apolonski, Appl. Phys. B 76, 329 (2003).
[CrossRef]

Torizuka, K.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

Udem, T.

V. S. Yakovlev, P. Dombi, G. Tempea, C. Lemell, J. Burgdörfer, T. Udem, and A. Apolonski, Appl. Phys. B 76, 329 (2003).
[CrossRef]

Udem, Th.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

van der Zande, W. J.

A. Guertler, F. Robicheaux, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 033002 (2004).
[CrossRef]

Villoresi, P.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Walther, H.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Yakovlev, V. S.

V. S. Yakovlev, P. Dombi, G. Tempea, C. Lemell, J. Burgdörfer, T. Udem, and A. Apolonski, Appl. Phys. B 76, 329 (2003).
[CrossRef]

Appl. Phys. B (1)

V. S. Yakovlev, P. Dombi, G. Tempea, C. Lemell, J. Burgdörfer, T. Udem, and A. Apolonski, Appl. Phys. B 76, 329 (2003).
[CrossRef]

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

Laser Phys. (1)

S. Chelkowski, N. H. Shon, and A. D. Bandrauk, Laser Phys. 13, 871 (2003).

Nature (1)

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. DeSilvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. A (1)

S. Chelkowski and A. D. Bandrauk, Phys. Rev. A 65, 061802 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

A. Guertler, F. Robicheaux, W. J. van der Zande, and L. D. Noordam, Phys. Rev. Lett. 92, 033002 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwart, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef]

T. M. Fortier, P. A. Ross, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Other (1)

S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A (to be published).

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Figures (3)

Fig. 1
Fig. 1

Asymmetry coefficient a as a function of the CE phase for laser intensity I=3.1×1013 W/cm2 and λ=800 nm for (a) various pulse durations ranging from τp=4.0 fs to τp=5.4 fs and (b) four central wavelengths λ: 778 nm I=3.7×1013 W/cm2, 800 nm, 840 nm 2.6×1013 W/cm2, and 1064 nm. τp=3.9 fs was used for all central wavelengths except λ=1064 nm, for which τp=5.2 fs was used to compensate for a longer period.

Fig. 2
Fig. 2

Asymmetry coefficient a as a function of the CE phase for λ=800 nm and τp=3.9 fs for various intensities ranging from I=3.1×1013 to 3×1014 W/cm2. The curve with squares shows the asymmetry a obtained after averaging of P± over the distribution of peak intensities in the focus with maximum peak intensity 1014 W/cm2.

Fig. 3
Fig. 3

Zero-asymmetry CE phase ϕ0 as a function of laser intensity.

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