Abstract

Numerical integrations of the two-dimensional Schrödinger equation that describes a flat atom interacting with an intense and linearly polarized laser field are presented. Simulations show the influence of the drift that is due to the magnetic field in situations in which a strong dichotomy of the wave function would otherwise have been expected.

© 1999 Optical Society of America

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References

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  1. J. H. Eberly, R. Grobe, C. K. Law, and Q. Su, “Numerical experiments in strong and super-strong fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).
  2. K. C. Kulander, K. J. Schafer, and J. L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).
  3. Q. Su, A. Sanpera, and L. Roso-Franco, “Atomic stabilization in the presence of intense laser pulses,” Int. J. Mod. Phys. B 8, 1655 (1994).
    [Crossref]
  4. M. Gavrila, “Atomic structure and decay in high frequency fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), and references therein.
  5. M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997), and references therein.
    [Crossref]
  6. A. Patel, N. J. Kylstra, and P. L. Knight, “Ellipticity and pulse shape dependence of localised wavepackets,” Opt. Express 4, 496–537 (1999).
    [Crossref] [PubMed]
  7. M. Protopapas, C. H. Keitel, and P. L. Knight, “Relativistic mass shift effects in adiabatic intense laser field stabilization of atoms,” J. Phys. B 29, L591–L598 (1996).
    [Crossref]
  8. C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A 51, 1420–1430 (1995).
    [Crossref] [PubMed]
  9. P. Moreno, “Harmonic generation by H and H2+ in intense laser pulses,” Ph. D. dissertation, (Universidad de Salamanca, Salamanca, Spain, 1997).
  10. A. D. Bandrauk and H. Shen, “Exponential split operator methods for solving coupled time-dependent Schrödinger equations,” J. Chem. Phys. 99, 1185–1193 (1993).
    [Crossref]

1999 (1)

1997 (1)

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997), and references therein.
[Crossref]

1996 (1)

M. Protopapas, C. H. Keitel, and P. L. Knight, “Relativistic mass shift effects in adiabatic intense laser field stabilization of atoms,” J. Phys. B 29, L591–L598 (1996).
[Crossref]

1995 (1)

C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A 51, 1420–1430 (1995).
[Crossref] [PubMed]

1994 (1)

Q. Su, A. Sanpera, and L. Roso-Franco, “Atomic stabilization in the presence of intense laser pulses,” Int. J. Mod. Phys. B 8, 1655 (1994).
[Crossref]

1993 (1)

A. D. Bandrauk and H. Shen, “Exponential split operator methods for solving coupled time-dependent Schrödinger equations,” J. Chem. Phys. 99, 1185–1193 (1993).
[Crossref]

Bandrauk, A. D.

A. D. Bandrauk and H. Shen, “Exponential split operator methods for solving coupled time-dependent Schrödinger equations,” J. Chem. Phys. 99, 1185–1193 (1993).
[Crossref]

Eberly, J. H.

J. H. Eberly, R. Grobe, C. K. Law, and Q. Su, “Numerical experiments in strong and super-strong fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).

Gavrila, M.

M. Gavrila, “Atomic structure and decay in high frequency fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), and references therein.

Grobe, R.

J. H. Eberly, R. Grobe, C. K. Law, and Q. Su, “Numerical experiments in strong and super-strong fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).

Keitel, C. H.

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997), and references therein.
[Crossref]

M. Protopapas, C. H. Keitel, and P. L. Knight, “Relativistic mass shift effects in adiabatic intense laser field stabilization of atoms,” J. Phys. B 29, L591–L598 (1996).
[Crossref]

C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A 51, 1420–1430 (1995).
[Crossref] [PubMed]

Knight, P. L.

A. Patel, N. J. Kylstra, and P. L. Knight, “Ellipticity and pulse shape dependence of localised wavepackets,” Opt. Express 4, 496–537 (1999).
[Crossref] [PubMed]

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997), and references therein.
[Crossref]

M. Protopapas, C. H. Keitel, and P. L. Knight, “Relativistic mass shift effects in adiabatic intense laser field stabilization of atoms,” J. Phys. B 29, L591–L598 (1996).
[Crossref]

C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A 51, 1420–1430 (1995).
[Crossref] [PubMed]

Krause, J. L.

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).

Kulander, K. C.

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).

Kylstra, N. J.

Law, C. K.

J. H. Eberly, R. Grobe, C. K. Law, and Q. Su, “Numerical experiments in strong and super-strong fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).

Moreno, P.

P. Moreno, “Harmonic generation by H and H2+ in intense laser pulses,” Ph. D. dissertation, (Universidad de Salamanca, Salamanca, Spain, 1997).

Patel, A.

Protopapas, M.

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997), and references therein.
[Crossref]

M. Protopapas, C. H. Keitel, and P. L. Knight, “Relativistic mass shift effects in adiabatic intense laser field stabilization of atoms,” J. Phys. B 29, L591–L598 (1996).
[Crossref]

Roso-Franco, L.

Q. Su, A. Sanpera, and L. Roso-Franco, “Atomic stabilization in the presence of intense laser pulses,” Int. J. Mod. Phys. B 8, 1655 (1994).
[Crossref]

Sanpera, A.

Q. Su, A. Sanpera, and L. Roso-Franco, “Atomic stabilization in the presence of intense laser pulses,” Int. J. Mod. Phys. B 8, 1655 (1994).
[Crossref]

Schafer, K. J.

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).

Shen, H.

A. D. Bandrauk and H. Shen, “Exponential split operator methods for solving coupled time-dependent Schrödinger equations,” J. Chem. Phys. 99, 1185–1193 (1993).
[Crossref]

Su, Q.

Q. Su, A. Sanpera, and L. Roso-Franco, “Atomic stabilization in the presence of intense laser pulses,” Int. J. Mod. Phys. B 8, 1655 (1994).
[Crossref]

J. H. Eberly, R. Grobe, C. K. Law, and Q. Su, “Numerical experiments in strong and super-strong fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).

Int. J. Mod. Phys. B (1)

Q. Su, A. Sanpera, and L. Roso-Franco, “Atomic stabilization in the presence of intense laser pulses,” Int. J. Mod. Phys. B 8, 1655 (1994).
[Crossref]

J. Chem. Phys. (1)

A. D. Bandrauk and H. Shen, “Exponential split operator methods for solving coupled time-dependent Schrödinger equations,” J. Chem. Phys. 99, 1185–1193 (1993).
[Crossref]

J. Phys. B (1)

M. Protopapas, C. H. Keitel, and P. L. Knight, “Relativistic mass shift effects in adiabatic intense laser field stabilization of atoms,” J. Phys. B 29, L591–L598 (1996).
[Crossref]

Opt. Express (1)

Phys. Rev. A (1)

C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A 51, 1420–1430 (1995).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997), and references therein.
[Crossref]

Other (4)

P. Moreno, “Harmonic generation by H and H2+ in intense laser pulses,” Ph. D. dissertation, (Universidad de Salamanca, Salamanca, Spain, 1997).

M. Gavrila, “Atomic structure and decay in high frequency fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), and references therein.

J. H. Eberly, R. Grobe, C. K. Law, and Q. Su, “Numerical experiments in strong and super-strong fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).

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Figures (1)

Figure 1.
Figure 1.

Probability density |Ψ(x, y, t)|2 of the electron after 10 cycles of the field for E 0=15 au (intensity, 7.9×1018 W/cm 2) and ωL =1 au (photon energy, 27 eV). A linear envelope four-cycles turn-on has been employed. (a) results obtained in the dipole approximation, (b) simulation including the space dependence of the fields [Eq. (5)]. In both cases, contour plot lines are set to the same linear scale.

Equations (10)

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i t Ψ ( r , t ) = [ 1 2 ( p + 1 c A ( r , t ) ) 2 + V ( r ) ] Ψ ( r , t ) ,
V ( x , y ) = 1 ( x 2 + y 2 + a ) 1 2 ,
E y ( x , t ) = E 0 f ( x , t ) sin ( kx ω L t ) ,
A y ( x , t ) = c 0 t E y ( x , t ) dt .
i t Ψ ( x , y , t ) = [ 1 2 ( 2 x 2 + 2 y 2 ) i c A y ( x , t ) y + 1 2 c 2 A y 2 ( x , t ) + V ( x , y ) ] Ψ ( x , y , t ) .
Ψ ( x , y , t + Δ t ) = exp [ i Δ t H ̂ ( t + Δ t 2 ) ] Ψ ( x , y , t )
exp [ i Δ t 2 H ̂ x ( t + Δ t 2 ) ] exp [ i Δ t H ̂ y ( t + Δ t 2 ) ]
× exp [ i Δ t 2 H ̂ x ( t + Δ t 2 ) ] Ψ ( x , y , t ) ,
H ̂ x ( t ) = 1 2 2 x 2 + 1 2 V ( x , y ) + 1 2 c 2 A y 2 ( x , t ) ,
H ̂ y ( t ) = 1 2 2 y 2 + 1 2 V ( x , y ) i c A y ( x , t ) y .

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