Abstract

A gas of rubidium atoms has been excited by a combination of ultraviolet and far-infrared excitation to a superposition of Stark states lying just above the classical saddle point. Using an atomic streak camera, we have demonstrated that the atom ejects an ultrafast train of electron subpulses nearly equally spaced in time, with a repetition rate of approximately 50 GHz. The frequency characteristics of this pulse train are seen to be extremely sensitive to small changes in the static electric field. These measurements imply that, by variation of the electric field during the electron emission, it is possible to create shaped ultrafast electron pulses analogous to shaped optical pulses.

© 1999 Optical Society of America

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  1. G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. Lett. 76, 1784 (1996).
    [CrossRef] [PubMed]
  2. G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. A 52, 2016 (1995).
    [CrossRef] [PubMed]
  3. C. Raman, T. C. Weinacht, and P. H. Bucksbaum, Phys. Rev. A 55, R3995 (1997).
    [CrossRef]
  4. F. Robicheaux and J. Shaw, Phys. Rev. Lett. 77, 4154 (1996).
    [CrossRef] [PubMed]
  5. F. Robicheaux and J. Shaw, Phys. Rev. A 56, 278 (1997).
    [CrossRef]
  6. For a review of the physics of Rydberg atoms, see, for example, Thomas F. Gallagher, Rydberg Atoms (Cambridge U. Press, Cambridge, UK, 1994).
  7. F. Robicheaux, G. M. Lankhuijzen, and L. D. Noordam, J. Opt. Soc. Am. B 15, 1 (1998).
    [CrossRef]
  8. H. E. Elsayed-Ali and J. W. Hermann, Rev. Sci. Instrum. 61, 1636 (1990).
    [CrossRef]
  9. J. C. Williamson, M. Dantus, S. B. Kim, and A. H. Zewail, Chem. Phys. Lett. 196, 529 (1992).
    [CrossRef]
  10. G. Farkas and C. Toth, Phys. Rev. A 41, 4123 (1990).
    [CrossRef] [PubMed]
  11. D. M. Riffe, X. Y. Wang, Michael C. Downer, D. L. Fisher, T. Tajima, J. L. Erskine, and R. M. More, “Femtosecond thermionic emission from metals in the space-charge-limited regime,” J. Opt. Soc. Am. B 10, 1424 (1993).
    [CrossRef]
  12. V. G. Minogin, M. V. Fedorov, and V. S. Letokhov, Opt. Commun. 140, 250 (1997).
    [CrossRef]
  13. G. M. Lankhuijzen, M. Drabbels, F. Robicheaux, and L. D. Noordam, Phys. Rev. A 57, 440 (1998).
    [CrossRef]
  14. A. M. Weiner, J. P. Heritage, and E. M. Kirschner, J. Opt. Soc. Am. B 5, 1563 (1988).
    [CrossRef]
  15. For a description of a Rydberg atom-based low-energy electron gun, see D. Klar, M.-W. Ruf, and H. Hotop, Meas. Sci. Technol. 5, 1248 (1994).
    [CrossRef]
  16. A detailed treatment of the theory of FEL operation can be found, for example, in C. A. Brau, Free Electron Lasers (Academic, Boston, Mass., 1990), 51ff.
  17. D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. Technol. 36, 297 (1995).
    [CrossRef]
  18. L. D. Noordam, A. ten Wolder, and A. Lagendijk, “Time dependence of an atomic electron wave function in an electrical field,” Phys. Rev. A 40, 6999 (1989).
    [CrossRef] [PubMed]
  19. G. M. Lankhuijzen, F. Robicheaux, and L. D. Noordam, Phys. Rev. Lett. 79, 2427 (1997).
    [CrossRef]
  20. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1992).

1998 (2)

F. Robicheaux, G. M. Lankhuijzen, and L. D. Noordam, J. Opt. Soc. Am. B 15, 1 (1998).
[CrossRef]

G. M. Lankhuijzen, M. Drabbels, F. Robicheaux, and L. D. Noordam, Phys. Rev. A 57, 440 (1998).
[CrossRef]

1997 (4)

F. Robicheaux and J. Shaw, Phys. Rev. A 56, 278 (1997).
[CrossRef]

V. G. Minogin, M. V. Fedorov, and V. S. Letokhov, Opt. Commun. 140, 250 (1997).
[CrossRef]

C. Raman, T. C. Weinacht, and P. H. Bucksbaum, Phys. Rev. A 55, R3995 (1997).
[CrossRef]

G. M. Lankhuijzen, F. Robicheaux, and L. D. Noordam, Phys. Rev. Lett. 79, 2427 (1997).
[CrossRef]

1996 (2)

F. Robicheaux and J. Shaw, Phys. Rev. Lett. 77, 4154 (1996).
[CrossRef] [PubMed]

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. Lett. 76, 1784 (1996).
[CrossRef] [PubMed]

1995 (2)

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. A 52, 2016 (1995).
[CrossRef] [PubMed]

D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. Technol. 36, 297 (1995).
[CrossRef]

1994 (1)

For a description of a Rydberg atom-based low-energy electron gun, see D. Klar, M.-W. Ruf, and H. Hotop, Meas. Sci. Technol. 5, 1248 (1994).
[CrossRef]

1993 (1)

1992 (1)

J. C. Williamson, M. Dantus, S. B. Kim, and A. H. Zewail, Chem. Phys. Lett. 196, 529 (1992).
[CrossRef]

1990 (2)

G. Farkas and C. Toth, Phys. Rev. A 41, 4123 (1990).
[CrossRef] [PubMed]

H. E. Elsayed-Ali and J. W. Hermann, Rev. Sci. Instrum. 61, 1636 (1990).
[CrossRef]

1989 (1)

L. D. Noordam, A. ten Wolder, and A. Lagendijk, “Time dependence of an atomic electron wave function in an electrical field,” Phys. Rev. A 40, 6999 (1989).
[CrossRef] [PubMed]

1988 (1)

Bucksbaum, P. H.

C. Raman, T. C. Weinacht, and P. H. Bucksbaum, Phys. Rev. A 55, R3995 (1997).
[CrossRef]

Dantus, M.

J. C. Williamson, M. Dantus, S. B. Kim, and A. H. Zewail, Chem. Phys. Lett. 196, 529 (1992).
[CrossRef]

Downer, Michael C.

Drabbels, M.

G. M. Lankhuijzen, M. Drabbels, F. Robicheaux, and L. D. Noordam, Phys. Rev. A 57, 440 (1998).
[CrossRef]

Elsayed-Ali, H. E.

H. E. Elsayed-Ali and J. W. Hermann, Rev. Sci. Instrum. 61, 1636 (1990).
[CrossRef]

Erskine, J. L.

Farkas, G.

G. Farkas and C. Toth, Phys. Rev. A 41, 4123 (1990).
[CrossRef] [PubMed]

Fedorov, M. V.

V. G. Minogin, M. V. Fedorov, and V. S. Letokhov, Opt. Commun. 140, 250 (1997).
[CrossRef]

Fisher, D. L.

Heritage, J. P.

Hermann, J. W.

H. E. Elsayed-Ali and J. W. Hermann, Rev. Sci. Instrum. 61, 1636 (1990).
[CrossRef]

Hotop, H.

For a description of a Rydberg atom-based low-energy electron gun, see D. Klar, M.-W. Ruf, and H. Hotop, Meas. Sci. Technol. 5, 1248 (1994).
[CrossRef]

Kim, S. B.

J. C. Williamson, M. Dantus, S. B. Kim, and A. H. Zewail, Chem. Phys. Lett. 196, 529 (1992).
[CrossRef]

Kirschner, E. M.

Klar, D.

For a description of a Rydberg atom-based low-energy electron gun, see D. Klar, M.-W. Ruf, and H. Hotop, Meas. Sci. Technol. 5, 1248 (1994).
[CrossRef]

Lagendijk, A.

L. D. Noordam, A. ten Wolder, and A. Lagendijk, “Time dependence of an atomic electron wave function in an electrical field,” Phys. Rev. A 40, 6999 (1989).
[CrossRef] [PubMed]

Lankhuijzen, G. M.

G. M. Lankhuijzen, M. Drabbels, F. Robicheaux, and L. D. Noordam, Phys. Rev. A 57, 440 (1998).
[CrossRef]

F. Robicheaux, G. M. Lankhuijzen, and L. D. Noordam, J. Opt. Soc. Am. B 15, 1 (1998).
[CrossRef]

G. M. Lankhuijzen, F. Robicheaux, and L. D. Noordam, Phys. Rev. Lett. 79, 2427 (1997).
[CrossRef]

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. Lett. 76, 1784 (1996).
[CrossRef] [PubMed]

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. A 52, 2016 (1995).
[CrossRef] [PubMed]

Letokhov, V. S.

V. G. Minogin, M. V. Fedorov, and V. S. Letokhov, Opt. Commun. 140, 250 (1997).
[CrossRef]

Minogin, V. G.

V. G. Minogin, M. V. Fedorov, and V. S. Letokhov, Opt. Commun. 140, 250 (1997).
[CrossRef]

More, R. M.

Noordam, L. D.

G. M. Lankhuijzen, M. Drabbels, F. Robicheaux, and L. D. Noordam, Phys. Rev. A 57, 440 (1998).
[CrossRef]

F. Robicheaux, G. M. Lankhuijzen, and L. D. Noordam, J. Opt. Soc. Am. B 15, 1 (1998).
[CrossRef]

G. M. Lankhuijzen, F. Robicheaux, and L. D. Noordam, Phys. Rev. Lett. 79, 2427 (1997).
[CrossRef]

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. Lett. 76, 1784 (1996).
[CrossRef] [PubMed]

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. A 52, 2016 (1995).
[CrossRef] [PubMed]

L. D. Noordam, A. ten Wolder, and A. Lagendijk, “Time dependence of an atomic electron wave function in an electrical field,” Phys. Rev. A 40, 6999 (1989).
[CrossRef] [PubMed]

Oepts, D.

D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. Technol. 36, 297 (1995).
[CrossRef]

Raman, C.

C. Raman, T. C. Weinacht, and P. H. Bucksbaum, Phys. Rev. A 55, R3995 (1997).
[CrossRef]

Riffe, D. M.

Robicheaux, F.

G. M. Lankhuijzen, M. Drabbels, F. Robicheaux, and L. D. Noordam, Phys. Rev. A 57, 440 (1998).
[CrossRef]

F. Robicheaux, G. M. Lankhuijzen, and L. D. Noordam, J. Opt. Soc. Am. B 15, 1 (1998).
[CrossRef]

F. Robicheaux and J. Shaw, Phys. Rev. A 56, 278 (1997).
[CrossRef]

G. M. Lankhuijzen, F. Robicheaux, and L. D. Noordam, Phys. Rev. Lett. 79, 2427 (1997).
[CrossRef]

F. Robicheaux and J. Shaw, Phys. Rev. Lett. 77, 4154 (1996).
[CrossRef] [PubMed]

Ruf, M.-W.

For a description of a Rydberg atom-based low-energy electron gun, see D. Klar, M.-W. Ruf, and H. Hotop, Meas. Sci. Technol. 5, 1248 (1994).
[CrossRef]

Shaw, J.

F. Robicheaux and J. Shaw, Phys. Rev. A 56, 278 (1997).
[CrossRef]

F. Robicheaux and J. Shaw, Phys. Rev. Lett. 77, 4154 (1996).
[CrossRef] [PubMed]

Tajima, T.

ten Wolder, A.

L. D. Noordam, A. ten Wolder, and A. Lagendijk, “Time dependence of an atomic electron wave function in an electrical field,” Phys. Rev. A 40, 6999 (1989).
[CrossRef] [PubMed]

Toth, C.

G. Farkas and C. Toth, Phys. Rev. A 41, 4123 (1990).
[CrossRef] [PubMed]

van Amersfoort, P. W.

D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. Technol. 36, 297 (1995).
[CrossRef]

van der Meer, A. F. G.

D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. Technol. 36, 297 (1995).
[CrossRef]

Wang, X. Y.

Weinacht, T. C.

C. Raman, T. C. Weinacht, and P. H. Bucksbaum, Phys. Rev. A 55, R3995 (1997).
[CrossRef]

Weiner, A. M.

Williamson, J. C.

J. C. Williamson, M. Dantus, S. B. Kim, and A. H. Zewail, Chem. Phys. Lett. 196, 529 (1992).
[CrossRef]

Zewail, A. H.

J. C. Williamson, M. Dantus, S. B. Kim, and A. H. Zewail, Chem. Phys. Lett. 196, 529 (1992).
[CrossRef]

Chem. Phys. Lett. (1)

J. C. Williamson, M. Dantus, S. B. Kim, and A. H. Zewail, Chem. Phys. Lett. 196, 529 (1992).
[CrossRef]

Infrared Phys. Technol. (1)

D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. Technol. 36, 297 (1995).
[CrossRef]

J. Opt. Soc. Am. B (3)

Meas. Sci. Technol. (1)

For a description of a Rydberg atom-based low-energy electron gun, see D. Klar, M.-W. Ruf, and H. Hotop, Meas. Sci. Technol. 5, 1248 (1994).
[CrossRef]

Opt. Commun. (1)

V. G. Minogin, M. V. Fedorov, and V. S. Letokhov, Opt. Commun. 140, 250 (1997).
[CrossRef]

Phys. Rev. A (6)

G. M. Lankhuijzen, M. Drabbels, F. Robicheaux, and L. D. Noordam, Phys. Rev. A 57, 440 (1998).
[CrossRef]

L. D. Noordam, A. ten Wolder, and A. Lagendijk, “Time dependence of an atomic electron wave function in an electrical field,” Phys. Rev. A 40, 6999 (1989).
[CrossRef] [PubMed]

G. Farkas and C. Toth, Phys. Rev. A 41, 4123 (1990).
[CrossRef] [PubMed]

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. A 52, 2016 (1995).
[CrossRef] [PubMed]

C. Raman, T. C. Weinacht, and P. H. Bucksbaum, Phys. Rev. A 55, R3995 (1997).
[CrossRef]

F. Robicheaux and J. Shaw, Phys. Rev. A 56, 278 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

F. Robicheaux and J. Shaw, Phys. Rev. Lett. 77, 4154 (1996).
[CrossRef] [PubMed]

G. M. Lankhuijzen, F. Robicheaux, and L. D. Noordam, Phys. Rev. Lett. 79, 2427 (1997).
[CrossRef]

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. Lett. 76, 1784 (1996).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

H. E. Elsayed-Ali and J. W. Hermann, Rev. Sci. Instrum. 61, 1636 (1990).
[CrossRef]

Other (3)

For a review of the physics of Rydberg atoms, see, for example, Thomas F. Gallagher, Rydberg Atoms (Cambridge U. Press, Cambridge, UK, 1994).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1992).

A detailed treatment of the theory of FEL operation can be found, for example, in C. A. Brau, Free Electron Lasers (Academic, Boston, Mass., 1990), 51ff.

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Figures (4)

Fig. 1
Fig. 1

Schematic showing the geometry of the interaction region and the basic operation of the atomic streak camera, together with a simple depiction of the optical excitation scheme.

Fig. 2
Fig. 2

Raw image, from the atomic streak camera, showing the modulated electron ionization due to a single ultrafast far-infrared pulse. The horizontal axis is distance parallel to the propagation of the laser beams, whereas the vertical axis represents the time axis due to the action of the time-varying electric field placed on the deflection plates. The image spans roughly 150 ps. This image was taken at a field strength of 1700 V/cm. The solid curves in the figure represent contours of constant time, with a separation of 30 ps between contours. At the right-hand side is a graph of the electron flux obtained by integration along contours of constant time.

Fig. 3
Fig. 3

Reconstructed ionization traces obtained at three different field strengths, respectively (from the top): 1690, 1700, and 1705 V/cm. All the other experimental parameters remained unchanged. The vertical dotted lines are provided to guide the eye. The observed variations in carrier frequency and envelope are due primarily to changes in the overlap between the excitation spectrum and the Stark state energies caused by the changing electric field.

Fig. 4
Fig. 4

Comparison between data collected at 1700 V/cm (shown in the central panel of Fig. 3) and theoretical modeling. The static electric field, the far-infrared laser center frequency, the bandwidth, and the chirp were varied within experimental uncertainty to yield reasonable agreement between model and data. Deviations between data and theory at long times is due to the extreme sensitivity of the experiment to small variations in the optical spectrum and the electric field (see text).

Equations (3)

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τ=2π3Fn,
iψ/t-Hψ=G(t)exp(-iωt)D exp(-iE0t)ψ0,
F(t)=ImdΩψ*(r, t)ψr(r, t),

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