Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions

Suppression of correlated electron escape indouble ionization in strong laser fields

B. Eckhardt 1, K. Sacha 2, J. Zakrzewski 2,J. S. Prauzner-Bechcicki 2

1 Philipps-Universitat Marburg,2 Jagiellonian University, Krakow

International Workshop on Atomic PhysicsNovember 26-30, 2007

MPIPKS Dresden

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 ionizationof metastable He

• Quantum simulation of double ionization of metastable He

• Double ionization of molecules

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 atomslaser pulses: 800 nm, 220 fs, 3.8 · 1014 W/cm2

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〉 =∑

αLMS

〈~k1, ~k2|αLMS〉〈αLMS |T |ψ〉

(M + S) odd ⇒ 〈~k1, ~k2|αLMS〉 = 0

if k1 = k2, θ1 = θ2 and |φ1 − φ2| = π.

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〉 =∑

αLMS

〈~k1, ~k2|αLMS〉〈αLMS |T |ψ〉

(M + S) odd ⇒ 〈~k1, ~k2|αLMS〉 = 0

if k1 = k2, θ1 = θ2 and |φ1 − φ2| = π.

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 = U = P exp(−i

∫ Td

0 dtH(t)/~)

H =~p2

1+~p22

2 − 2r1− 2

r2+ 1

|~r1−~r2| + F (t)(z1 + z2)

⇒ M + S = const

For |ψ〉 being the metastable state of He where M = 0 and S = 1:

(M + S) odd ⇒ 〈~k1, ~k2|U|ψ〉 = 0 if:

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 = U = P exp(−i

∫ Td

0 dtH(t)/~)

H =~p2

1+~p22

2 − 2r1− 2

r2+ 1

|~r1−~r2| + F (t)(z1 + z2)

⇒ M + S = const

For |ψ〉 being the metastable state of He where M = 0 and S = 1:

(M + S) odd ⇒ 〈~k1, ~k2|U|ψ〉 = 0 if:

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 = U = P exp(−i

∫ Td

0 dtH(t)/~)

H =~p2

1+~p22

2 − 2r1− 2

r2+ 1

|~r1−~r2| + F (t)(z1 + z2)

⇒ M + S = const

For |ψ〉 being the metastable state of He where M = 0 and S = 1:

(M + S) odd ⇒ 〈~k1, ~k2|U|ψ〉 = 0 if:

Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions

Symmetric subspace:Sacha & Eckhardt, PRA 63 043414 (2001)

H =p2

1 + p22

2− 2

r1− 2

r2+

1

|r1 − r2|+ F (t)(z1 + z2)

z1 = z2 = zx1 = −x2 = x

⇒ V (x , z ; t) = − 4√x2 + z2

+1

2|x |+ 2F (t)z

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):

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):

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):

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.

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.

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.

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)

N2:

Zeidler et al., PRL 95, 203300 (2005)

〈~k1, ~k2|T |ψ〉 =∑

αLMS

〈~k1, ~k2|αLMS〉〈αLMS |T |ψ〉

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)

N2:

Zeidler et al., PRL 95, 203300 (2005)

〈~k1, ~k2|T |ψ〉 =∑

αLMS

〈~k1, ~k2|αLMS〉〈αLMS |T |ψ〉

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)

N2:

Zeidler et al., PRL 95, 203300 (2005)

〈~k1, ~k2|T |ψ〉 =∑

αLMS

〈~k1, ~k2|αLMS〉〈αLMS |T |ψ〉

Starting point Selection rules Suppression. . . Symmetric subspace Quantum simulations Diatomic molecules Conclusions

Conclusions:

• We have analyzed suppression of correlated electron escape indouble ionization of metastable He atoms by strong laserpulses

• In double ionization of molecules one may expect the similarsuppression, e.g. for O2 oriented along the polarization axis.