Abstract

An approach to electron correlation effects in atoms that uses quantum trajectories is presented. A comparison with the exact quantum mechanical results for 1D Helium atom shows that the major features of the correlated ground state distribution and of the strong field ionization dynamics are reproduced with quantum trajectories. The intra-atomic resonant transitions are described accurately by a trajectory ensemble. The present approach reduces significantly the computational time and it can be used for both bound and ionizing electrons.

© 2006 Optical Society of America

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Comparing classical and quantum dynamics of strong-field double ionization

R. Panfili, J. H. Eberly, and S. L. Haan
Opt. Express 8(7) 431-435 (2001)

References

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  1. K. Kulander, K. Shafer, and J. Krause, “Time dependent studies of multiphoton processes,” in Atoms in Intense Laser Fields,M. Gavrila, ed. (Academic Press, New York, 1992).
  2. S. L. Haan, R. Grobe, and J. H. Eberly, “Numerical study of autoionizing states in completely correlated two-electron systems,” Phys. Rev. A 50, 378–380 (1994).
    [Crossref] [PubMed]
  3. M. Petersilka and E. K. U. Gross, “Strong-field double ionization of helium: a density-functional perspective,” Laser Physics 9, 1–10 (1999).
  4. D. G. Lappas and R. van Leeuwen, “Electron correlation effects in the double ionization of He,” J. Phys. B: At. Mol. Opt. Phys. 31, L249–L256 (1998).
    [Crossref]
  5. M.H. Beck, A. Jackle, G.A Worth, and H.-D. Meyer, “The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets,” Physics Reports 324, 1–105 (2000).
    [Crossref]
  6. J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi, “An MCTDHF approach to multielectron dynamics in laser fields,” Laser Physics 13, 1064–1068 (2003).
  7. P. J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett. 94, 093002–1 (2005).
    [Crossref] [PubMed]
  8. R. Grobe and J. H. Eberly, “One-dimensional model of a negative ion and its interaction with laser fields,” Phys. Rev. A 48, 4664–4681 (1993).
    [Crossref] [PubMed]
  9. P. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).

2005 (1)

P. J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett. 94, 093002–1 (2005).
[Crossref] [PubMed]

2003 (1)

J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi, “An MCTDHF approach to multielectron dynamics in laser fields,” Laser Physics 13, 1064–1068 (2003).

2000 (1)

M.H. Beck, A. Jackle, G.A Worth, and H.-D. Meyer, “The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets,” Physics Reports 324, 1–105 (2000).
[Crossref]

1999 (1)

M. Petersilka and E. K. U. Gross, “Strong-field double ionization of helium: a density-functional perspective,” Laser Physics 9, 1–10 (1999).

1998 (1)

D. G. Lappas and R. van Leeuwen, “Electron correlation effects in the double ionization of He,” J. Phys. B: At. Mol. Opt. Phys. 31, L249–L256 (1998).
[Crossref]

1994 (1)

S. L. Haan, R. Grobe, and J. H. Eberly, “Numerical study of autoionizing states in completely correlated two-electron systems,” Phys. Rev. A 50, 378–380 (1994).
[Crossref] [PubMed]

1993 (2)

R. Grobe and J. H. Eberly, “One-dimensional model of a negative ion and its interaction with laser fields,” Phys. Rev. A 48, 4664–4681 (1993).
[Crossref] [PubMed]

P. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).

Beck, M.H.

M.H. Beck, A. Jackle, G.A Worth, and H.-D. Meyer, “The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets,” Physics Reports 324, 1–105 (2000).
[Crossref]

Brabec, T.

J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi, “An MCTDHF approach to multielectron dynamics in laser fields,” Laser Physics 13, 1064–1068 (2003).

Eberly, J. H.

P. J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett. 94, 093002–1 (2005).
[Crossref] [PubMed]

S. L. Haan, R. Grobe, and J. H. Eberly, “Numerical study of autoionizing states in completely correlated two-electron systems,” Phys. Rev. A 50, 378–380 (1994).
[Crossref] [PubMed]

R. Grobe and J. H. Eberly, “One-dimensional model of a negative ion and its interaction with laser fields,” Phys. Rev. A 48, 4664–4681 (1993).
[Crossref] [PubMed]

Fabian, C.

J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi, “An MCTDHF approach to multielectron dynamics in laser fields,” Laser Physics 13, 1064–1068 (2003).

Grobe, R.

S. L. Haan, R. Grobe, and J. H. Eberly, “Numerical study of autoionizing states in completely correlated two-electron systems,” Phys. Rev. A 50, 378–380 (1994).
[Crossref] [PubMed]

R. Grobe and J. H. Eberly, “One-dimensional model of a negative ion and its interaction with laser fields,” Phys. Rev. A 48, 4664–4681 (1993).
[Crossref] [PubMed]

Gross, E. K. U.

M. Petersilka and E. K. U. Gross, “Strong-field double ionization of helium: a density-functional perspective,” Laser Physics 9, 1–10 (1999).

Haan, S. L.

P. J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett. 94, 093002–1 (2005).
[Crossref] [PubMed]

S. L. Haan, R. Grobe, and J. H. Eberly, “Numerical study of autoionizing states in completely correlated two-electron systems,” Phys. Rev. A 50, 378–380 (1994).
[Crossref] [PubMed]

Ho, P. J.

P. J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett. 94, 093002–1 (2005).
[Crossref] [PubMed]

Holland, P.

P. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).

Jackle, A.

M.H. Beck, A. Jackle, G.A Worth, and H.-D. Meyer, “The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets,” Physics Reports 324, 1–105 (2000).
[Crossref]

Kitzler, M.

J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi, “An MCTDHF approach to multielectron dynamics in laser fields,” Laser Physics 13, 1064–1068 (2003).

Krause, J.

K. Kulander, K. Shafer, and J. Krause, “Time dependent studies of multiphoton processes,” in Atoms in Intense Laser Fields,M. Gavrila, ed. (Academic Press, New York, 1992).

Kulander, K.

K. Kulander, K. Shafer, and J. Krause, “Time dependent studies of multiphoton processes,” in Atoms in Intense Laser Fields,M. Gavrila, ed. (Academic Press, New York, 1992).

Lappas, D. G.

D. G. Lappas and R. van Leeuwen, “Electron correlation effects in the double ionization of He,” J. Phys. B: At. Mol. Opt. Phys. 31, L249–L256 (1998).
[Crossref]

Leeuwen, R. van

D. G. Lappas and R. van Leeuwen, “Electron correlation effects in the double ionization of He,” J. Phys. B: At. Mol. Opt. Phys. 31, L249–L256 (1998).
[Crossref]

Meyer, H.-D.

M.H. Beck, A. Jackle, G.A Worth, and H.-D. Meyer, “The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets,” Physics Reports 324, 1–105 (2000).
[Crossref]

Panfili, R.

P. J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett. 94, 093002–1 (2005).
[Crossref] [PubMed]

Petersilka, M.

M. Petersilka and E. K. U. Gross, “Strong-field double ionization of helium: a density-functional perspective,” Laser Physics 9, 1–10 (1999).

Scrinzi, A.

J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi, “An MCTDHF approach to multielectron dynamics in laser fields,” Laser Physics 13, 1064–1068 (2003).

Shafer, K.

K. Kulander, K. Shafer, and J. Krause, “Time dependent studies of multiphoton processes,” in Atoms in Intense Laser Fields,M. Gavrila, ed. (Academic Press, New York, 1992).

Worth, G.A

M.H. Beck, A. Jackle, G.A Worth, and H.-D. Meyer, “The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets,” Physics Reports 324, 1–105 (2000).
[Crossref]

Zanghellini, J.

J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi, “An MCTDHF approach to multielectron dynamics in laser fields,” Laser Physics 13, 1064–1068 (2003).

J. Phys. B: At. Mol. Opt. Phys. (1)

D. G. Lappas and R. van Leeuwen, “Electron correlation effects in the double ionization of He,” J. Phys. B: At. Mol. Opt. Phys. 31, L249–L256 (1998).
[Crossref]

Laser Physics (2)

J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi, “An MCTDHF approach to multielectron dynamics in laser fields,” Laser Physics 13, 1064–1068 (2003).

M. Petersilka and E. K. U. Gross, “Strong-field double ionization of helium: a density-functional perspective,” Laser Physics 9, 1–10 (1999).

Phys. Rev. A (2)

R. Grobe and J. H. Eberly, “One-dimensional model of a negative ion and its interaction with laser fields,” Phys. Rev. A 48, 4664–4681 (1993).
[Crossref] [PubMed]

S. L. Haan, R. Grobe, and J. H. Eberly, “Numerical study of autoionizing states in completely correlated two-electron systems,” Phys. Rev. A 50, 378–380 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

P. J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett. 94, 093002–1 (2005).
[Crossref] [PubMed]

Physics Reports (1)

M.H. Beck, A. Jackle, G.A Worth, and H.-D. Meyer, “The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets,” Physics Reports 324, 1–105 (2000).
[Crossref]

Other (2)

K. Kulander, K. Shafer, and J. Krause, “Time dependent studies of multiphoton processes,” in Atoms in Intense Laser Fields,M. Gavrila, ed. (Academic Press, New York, 1992).

P. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).

Supplementary Material (3)

» Media 1: MOV (530 KB)     
» Media 2: MOV (1347 KB)     
» Media 3: MOV (344 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Ground state of the Hydrogen 1D model atom (left). Blue-exact wave function, red-quantum trajectory distribution. The movie (531 KB) shows the evolution from the ground state to the first excited state. 10 000 quantum trajectories are used.

Fig. 2.
Fig. 2.

Singlet ground state calculation for 1D Helium. The left hand image shows the distribution of 10 000 two-particle coordinates after steady-state of the quantum trajectories is established. The right hand image shows the same distribution after interpolation with Gaussians. Here a=b=1.

Fig. 3.
Fig. 3.

Position space distributions for exact (left) and quantum trajectories (right) simulation of the strong field ionization of 1D Helium atom, three cycles after the pulse turn on. The movies associated with these pictures (1.3 MB, and 345 KB) show the time evolution of the two distributions. Here a=1, b=1.22.

Fig. 4.
Fig. 4.

The double-ionization yield calculated for six-cycle laser pulse at frequency 0.183 a.u. The red line shows the quantum trajectory result while the black line shows the exact result.

Equations (5)

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i t ψ ( x 1 , x 2 , t ) = [ H 0 + iA ( t ) ( x 1 + x 2 ) ] ψ ( x 1 , x 2 , t ) ,
H 0 = 1 2 2 x 1 2 1 2 2 x 2 2 2 a 2 + x 1 2 2 a 2 + x 2 2 + 1 b 2 + ( x 1 x 2 ) 2
i t φ i ( x i , t ) = [ 1 2 2 x i 2 2 a 2 + x i 2 + d x j φ j ( x j , t ) 2 b 2 + ( x i x j ) 2 + iA ( t ) x i ] φ i ( x i , t )
i t φ i k ( x i , t ) = [ 1 2 2 x i 2 2 a 2 + x i 2 + 1 b 2 + [ x i x j k ( t ) ] 2 + iA ( t ) x i ] φ i k ( x i , t )
d x i k dt v i k ( x i , t ) = Im [ 1 ψ ( x i , x j , t ) ψ ( x i , x j , t ) x i ] x i = x i k ( t ) ; x j = x j k ( t ) A ( t )

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