Abstract

We calculate the energy spectrum of electrons ejected from a model two-electron atom exposed to an intense laser pulse and follow the spectrum’s evolution in time. For the case of 13-photon double ionization, we see the appearance of above-threshold ionization peaks soon after the laser pulse reaches maximum intensity.

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References

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  1. D.N.Fittinghoff, P.R.Bolton, B.Chang, and K.C.Kulander, "Observation of nonsequential double ionization of helium with optical tunneling," Phys. Rev. Lett. 69, 2642-2645 (1992).
    [CrossRef] [PubMed]
  2. B.Walker, B.Sheehy, L.F.DiMauro, P.Agostini, K.J.Schafer, and K.C.Kulander, "Precision measurement of strong field double ionization of helium," Phys. Rev. Lett. 73, 1227-1230 (1994).
    [CrossRef] [PubMed]
  3. B.Sheehy, R.Lafon, M.Widmer, B.Walker, L.F.DiMauro, P.A.Agostini, and K.C.Kulander, "Single- and multiple-electron dynamics in the strong-field tunneling limit," Phys. Rev. A 58, 3942-3952 (1998).
    [CrossRef]
  4. J.H.Eberly, J.Javanainen and K.Rzazaewski, "Above-threshold ionization," Phys. Rep. 204, 331-383 (1991).
    [CrossRef]
  5. J.S. Parker, L.R. Moore, D. Dundas and K.T. Taylor, "Double ionization of helium at 390 nm," J. Phys. B 33, L691-L698 (2000).
    [CrossRef]
  6. C. Szymanowski, R. Panfili, W.-C. Liu, S.L. Haan, and J.H. Eberly, "Role of the correlation charge in the double ionization of two-electron model atoms exposed to intense laser fields," Phys. Rev. A 61, 055401 (2000) (4 pages).
    [CrossRef]
  7. Q. Su and J.H. Eberly, "Model atom for multiphoton physics," Phys. Rev. A 44, 5997-6008 (1991).
    [CrossRef] [PubMed]
  8. M.D. Feit, J.A. Fleck, Jr., and A. Steiger, "Solution of the Schroedinger Equation by a Spectral Method," J. Comput. Phys. 47, 412-433 (1982).
    [CrossRef]
  9. R. Grobe, S.L. Haan, and J.H. Eberly, "A split-domain algorithm for time-dependent multi-electron wave functions," Comp. Phys. Commun. 117, 200-210 (1999).
    [CrossRef]
  10. R. Panfili, C. Szymanowski, W.-C. Liu and J.H. Eberly, NATO Advanced Research Workshop on Super-Intense Laser-Atom Physics, Han-sur-Lesse, Belgium (2000).
  11. J.S. Parker, L.R. Moore, K.J. Meharg, D. Dundas and K.T. Taylor, "Double-electron above threshold ionization of helium," J. Phys. B 34, L69-L78 (2001).
    [CrossRef]

Other

D.N.Fittinghoff, P.R.Bolton, B.Chang, and K.C.Kulander, "Observation of nonsequential double ionization of helium with optical tunneling," Phys. Rev. Lett. 69, 2642-2645 (1992).
[CrossRef] [PubMed]

B.Walker, B.Sheehy, L.F.DiMauro, P.Agostini, K.J.Schafer, and K.C.Kulander, "Precision measurement of strong field double ionization of helium," Phys. Rev. Lett. 73, 1227-1230 (1994).
[CrossRef] [PubMed]

B.Sheehy, R.Lafon, M.Widmer, B.Walker, L.F.DiMauro, P.A.Agostini, and K.C.Kulander, "Single- and multiple-electron dynamics in the strong-field tunneling limit," Phys. Rev. A 58, 3942-3952 (1998).
[CrossRef]

J.H.Eberly, J.Javanainen and K.Rzazaewski, "Above-threshold ionization," Phys. Rep. 204, 331-383 (1991).
[CrossRef]

J.S. Parker, L.R. Moore, D. Dundas and K.T. Taylor, "Double ionization of helium at 390 nm," J. Phys. B 33, L691-L698 (2000).
[CrossRef]

C. Szymanowski, R. Panfili, W.-C. Liu, S.L. Haan, and J.H. Eberly, "Role of the correlation charge in the double ionization of two-electron model atoms exposed to intense laser fields," Phys. Rev. A 61, 055401 (2000) (4 pages).
[CrossRef]

Q. Su and J.H. Eberly, "Model atom for multiphoton physics," Phys. Rev. A 44, 5997-6008 (1991).
[CrossRef] [PubMed]

M.D. Feit, J.A. Fleck, Jr., and A. Steiger, "Solution of the Schroedinger Equation by a Spectral Method," J. Comput. Phys. 47, 412-433 (1982).
[CrossRef]

R. Grobe, S.L. Haan, and J.H. Eberly, "A split-domain algorithm for time-dependent multi-electron wave functions," Comp. Phys. Commun. 117, 200-210 (1999).
[CrossRef]

R. Panfili, C. Szymanowski, W.-C. Liu and J.H. Eberly, NATO Advanced Research Workshop on Super-Intense Laser-Atom Physics, Han-sur-Lesse, Belgium (2000).

J.S. Parker, L.R. Moore, K.J. Meharg, D. Dundas and K.T. Taylor, "Double-electron above threshold ionization of helium," J. Phys. B 34, L69-L78 (2001).
[CrossRef]

Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1.

(1.3 MB) Movie of the electron energy distribution at different times during the evolution of an initial ground state wave function in the presence of a laser field. The laser pulse is ten cycles long with a two-cycle linear turn-on and turn-off. The laser frequency is ω=0.1837 a.u. and its maximum intensity is 5.5×1014W/cm2. Snapshots are taken every half-cycle on the quarter cycle and the distribution is plotted on a logarithmic scale as a function of electron energy as defined in Eq. (4) divided by photon energy. The still frame of the movie shows the final energy distribution immediately after the pulse has been turned off.

Fig. 2.
Fig. 2.

Time evolution of the electron energy spectrum during a laser pulse with frequency 0.1837 a.u., intensity 5.5×1014W/cm2, and a pulse envelope with a two cycle turn on and off and a six cycle plateau. An ATI series appears by 3.75 laser cycles and becomes sharper as the pulse progresses in time.

Fig. 3.
Fig. 3.

Energy spectra at the end of a laser pulse. Each laser pulse has fixed intensity (5.5×1014W/cm2), frequency (0.1837 a.u.), turn-on and turn-off times (2 cycles). The only parameter being varied is the time spent at maximum intensity.

Fig. 4.
Fig. 4.

Predicted versus calculated peak positions for a six cycle pulse with laser frequency 0.1837 a.u. and a series of different intensities. The intensity used to calculate the Stark shift and pondermotive potential in our theoretical model is the cycle-averaged laser intensity or half of the peak intensity. Each line has been moved downward a uniform 0.3a.u. in order to clearly show how the ATI peaks trend with changes in intensity.

Fig. 5.
Fig. 5.

ATI spectra at the end of an eight cycle laser pulse for a variety of laser intensities. We can clearly see the ATI peaks shifting in energy as the laser intensity is increased.

Equations (7)

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

V ( r ) = 1 r V ( x ) = 1 x 2 + 1
𝓗 = p 1 2 2 + p 2 2 2 2 V ( x 1 ) 2 V ( x 2 ) + V ( x 1 x 2 ) + ( x 1 + x 2 ) E ( t ) ,
E ( t ) = E o f ( t ) sin ( ω t + ϕ ) .
E n = p n p n × p n 2 2
Δ E m = E m + 1 - E m 1 2 = 1 2 p m + 1 p m + 1 × p m + 1 2 2 p m 1 p m 1 × p m 1 2 2
ψ ( E m , E n ) = ψ ( p m , p n ) Δ E m Δ E n .
Ψ ( p ) = ψ ( p 1 , p ) d p 1 = ψ ( p , p 2 ) d p 2

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