1. Electron Momentum Distributions in Short-Pulse Double Ionization -- Agreement with a Classical Model in 3D S.L. Haan, A. Karim (presenter), and L. Breen Calvin College Grand Rapids MI 49546 J.H. Eberly University of Rochester Rochester NY 14627 Work supported by Calvin College, NSF, and DOE AK conference attendance supported by APS

2. We study double ionization of two electron atoms in strong laser fields using ensembles of 400,000 3D classical model atoms. This talk will emphasize results rather than technique. --will summarize results presented in S.L. Haan, L. Breen, A. Karim, and J.H. Eberly, submitted Laser parameters: –wavelength 780 nm –Linearly polarized in z direction –For results we’ll show today, we use a 10-cycle trapezoidal pulse with 2 cycle turn-on and 2-cycle turn off.

3. Final Momenta of ionized electron pairs Plot final momentum along direction of laser polarization for one ionized electron vs. the other Preference for quadrants 1 and 3 (same-momentum hemisphere), but population is present in all 4 quadrants Having population in all 4 quadrants is consistent with experiment--and different from predictions of most theoretical treatments I=.2 PW/cm 2 I=.4 PW/cm 2 I=.6 PW/cm 2 I=.8 PW/cm 2

4. Cause of opposite hemisphere emissions? We can backtrack doubly ionizing trajectories to learn cause! Trajectories show recollision typically followed by a short time delay before final ionization. Careful sorting… Recollision time -- time of closest approach of two electrons after first electron achieves E>0. Double ionization time -- time at which both electrons achieve E>0 or both escape nuclear well.

5. Delay time: recollision to double ionization Most DI trajectories show a part-cycle phase delay between recollision and double ionization –Less than 15% show “nearly immediate ionization” after recollision. –Nonetheless, for I≥.4 PW/cm 2, over half the DI occurs within 1/3 cycle of recollision.

6. Final momenta sorted by: delay times from recollision to ionization and by final direction relative to recollision direction delay<1/25 cycle delay<1/4 cycle delay<1/2 cycledelay≥1/2 cycle RE directions--adjust signs of momenta so all collisions occur with returning electron traveling in the +z direction. For small delay times, almost all emergences are opposite from the recollision direction. With increased delay times, there is increased spillover into the 2nd and 4th quadrants. I=6x10 14 W/cm 2

7. Final momenta sorted by: delay times from recollision to ionization and by final direction relative to recollision direction delay<1/25 cycle delay<1/4 cycle delay<1/2 cycledelay≥1/2 cycle RE directions--adjust signs of momenta so all collisions occur with returning electron traveling in the +z direction. For small delay times, almost all emergences are opposite from the recollision direction. With increased delay times, there is increased spillover into the 2nd and 4th quadrants. I=6x10 14 W/cm 2

8. So… Q: When in the laser cycle do the recollisions and ionizations typically occur? –Simpleman model: The most energetic recollision events occur just before a laser zero –(e.g. Corkum 71, 1994 (1993)) –The confining potential-energy barrier is most suppressed when the field is maximal a quarter cycle later

9. # of recollisions and ionizations vs. laser phase Background curve shows laser cycle. Red--double ionization within 1/4 cycle of recollision and emergence in same momentum hemisphere Green--similar, but emerge in opposite momentum hemispheres Blue--remaining DI trajectories (i.e., delay time > 1/4 cycle). Collisions peak just before a zero of the laser (bins 5 & 10). But Ionizations peak just before the laser reaches full strength (bins 2- 3 & 7-8). Inference: Recollisions near zeros produce an excited complex that typically ionizes during the next laser maximum (laser phase bin #)

10. Of drift velocities Drift velocity for an electron exposed to an oscillating force -eE 0 sin(  t) is v π/2 = v 0 − eE 0 /(mω) where v 0 = instantaneous velocity at ωt = 0 v π/2 = instantaneous velocity at ωt = π/2 and = drift velocity So, suppose recollision occurs in + direction at ωt = nπ and an electron is free just after collision with velocity v 0 > 0 –laser force has just been in + direction and will now begin pushing in the - direction –Drift velocity for that electron is v π/2 = v 0 − eE 0 /(mω) Partial cancellation  Maximum value for |v π/2 | = eE 0 /(mω)

11. Our description of the DI process Up to about 15% of the time (depending on intensity), recollision leads nearly immediately to double ionization. Recollisions most often occur as laser field passes through zero; both electrons have small speed immediately after collision (< eE 0 /(mω) ) and are pushed back opposite from the recollision direction Aside -- often returning electron misses on first return V drift = v(  t=  /2+n  ) laser force Because of the direction change, the maximum drift speed for either electron is eE 0 /(mω)

12. In most cases there is a time lag between recollision and the ionization of the second electron If second electron ionizes before laser peaks then (to first approximation) it can follow the other electron out in the negative direction (opposite from the recollision direction) laser force V drift = v(  t=  /2+n  ) But if the phase delay is too great (to first approx, electron emergence after the field peaks), the electrons can have drift velocities in opposite momentum hemispheres. laser force