1) The document discusses selection rules in double ionization of atoms and the suppression of correlated electron escape in double ionization of metastable helium. 2) It examines using a symmetric subspace and quantum simulations to model double ionization, showing suppression for a 800nm single-cycle laser pulse. 3) Double ionization of molecules like N2 and O2 is also discussed, with the conclusion that similar suppression may occur for oriented O2.

1. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Suppression of correlated electron escape in
double ionization in strong laser fields
B. Eckhardt 1 , K. Sacha 2 , J. Zakrzewski 2 ,
J. S. Prauzner-Bechcicki 2
1 Philipps-Universit¨t Marburg,
a
2 Jagiellonian University, Krak´w
o
International Workshop on Atomic Physics
November 26-30, 2007
MPIPKS Dresden

2. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Plan:
• Selection rules in double ionization of atoms
• Suppression of correlated electron escape in double ionization
of metastable He
• Quantum simulation of double ionization of metastable He
• Double ionization of molecules

3. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Correlated electron escape:
T. Weber et al., Nature 405, 658 (2000)
Double ionization of Ar atoms
laser pulses: 800 nm, 220 fs, 3.8 · 1014 W/cm2

4. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Maulbetsch & Briggs selection rules:
F. Maulbetsch & J. S. Briggs, JPB 28, 551 (1995)
k1 , k2 |T |ψ = k1 , k2 |αLMS αLMS|T |ψ
αLMS

5. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Maulbetsch & Briggs selection rules:
F. Maulbetsch & J. S. Briggs, JPB 28, 551 (1995)
k1 , k2 |T |ψ = k1 , k2 |αLMS αLMS|T |ψ
αLMS
(M + S) odd ⇒ k1 , k2 |αLMS = 0
if k1 = k2 , θ1 = θ2 and |φ1 − φ2 | = π.

6. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Suppression of correlated electron escape:
Eckhardt et al., to appear in PRA 76
For strong field multiphoton double ionization:
Td
T = U = P exp −i 0 dtH(t)/
2 2
p1 +p2 2 2 1
H= 2 − r1 − r2 + |r1 −r2 | + F (t)(z1 + z2 )

7. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Suppression of correlated electron escape:
Eckhardt et al., to appear in PRA 76
For strong field multiphoton double ionization:

T
T = U = P exp −i 0 d dtH(t)/ 
2 2
p1 +p2
⇒ M + S = const
H= 2 − r2 − r2 + |r1 −r2 |
1 2
1
+ F (t)(z1 + z2 ) 

8. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Suppression of correlated electron escape:
Eckhardt et al., to appear in PRA 76
For strong field multiphoton double ionization:

T
T = U = P exp −i 0 d dtH(t)/ 
2 2
p1 +p2
⇒ M + S = const
H= 2 − r2 − r2 + |r1 −r2 |
1 2
1
+ F (t)(z1 + z2 ) 
For |ψ being the metastable state of He where M = 0 and S = 1:
(M + S) odd ⇒ k1 , k2 |U|ψ = 0 if:

9. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Symmetric subspace:
Sacha & Eckhardt, PRA 63 043414 (2001)
p2 + p2
1 2 2 2 1
H= − − + + F (t)(z1 + z2 )
2 r1 r2 |r1 − r2 |
z1 = z2 = z 4 1
⇒ V (x, z; t) = − √ + + 2F (t)z
x1 = −x2 = x x 2 + z 2 2|x|

10. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Reduction of the dimensionality:
Eckhardt & Sacha, JPB 39 3865 (2006);
Prauzner-Bechcicki et al., PRL 98, 203002 (2007)

11. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Reduction of the dimensionality:
Eckhardt & Sacha, JPB 39 3865 (2006);
Prauzner-Bechcicki et al., PRL 98, 203002 (2007)
the present model V (r1 , r2 ):

12. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Reduction of the dimensionality:
Eckhardt & Sacha, JPB 39 3865 (2006);
Prauzner-Bechcicki et al., PRL 98, 203002 (2007)
the present model V (r1 , r2 ): the aligned electron model V (r1 , r2 ):

13. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Quantum simulations:
Eckhardt et al., to appear in PRA 76
800 nm, single cycle pulse, F = 0.15 a.u.

14. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Quantum simulations:
Eckhardt et al., to appear in PRA 76
800 nm, single cycle pulse, F = 0.15 a.u.

15. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Quantum simulations:
Eckhardt et al., to appear in PRA 76
800 nm, single cycle pulse, F = 0.15 a.u.
∆p = 0.07 a.u.

16. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Double ionization of N2 and O2 molecules:
N2 : O2 :
Eremina et al., PRL 92, 173001 (2004)

17. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Double ionization of N2 and O2 molecules:
N2 :
N2 : O2 :
Eremina et al., PRL 92, 173001 (2004)
Zeidler et al., PRL 95, 203300 (2005)

18. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Double ionization of N2 and O2 molecules:
N2 :
N2 : O2 :
Eremina et al., PRL 92, 173001 (2004)
Zeidler et al., PRL 95, 203300 (2005)
k1 , k2 |T |ψ = k1 , k2 |αLMS αLMS|T |ψ
αLMS

19. Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions
Conclusions:
• We have analyzed suppression of correlated electron escape in
double ionization of metastable He atoms by strong laser
pulses
• In double ionization of molecules one may expect the similar
suppression, e.g. for O2 oriented along the polarization axis.