Recollision, Time Delay, and Double Ionization studied with 3-D Classical Ensembles

S.L. Haan, A. Karim, and Z. Smith J.H. EberlyCalvin College University of RochesterGrand Rapids MI USA Rochester NY USA

Also acknowledging contributions ofC. Cully, A. Vache, D. Tannor, and L. Breen of Calvin CollegeR. Panfili of U. Rochester

in helping develop the 3-D ensemble program and technique

& Phay Ho (UR) for numerous discussions regarding double ionization

Work supported by National Science Foundation Grant PHY-0355035 and DOE Grant DE-FG02-05ER15713

• We set up an ensemble of classical two-electron atoms.– Each atom has slightly different initial conditions– Ensemble sizes 400,000

• We evolve each two-electron atom in time through a laser pulse, using Newton’s laws of motion.

• After each run, we can sort the trajectories and– Study statistical behavior;– Backtrack individual trajectories to learn their history.

Overview of Method

Some Details

– To prevent self-ionization of our starting state, we shield the electron-nucleus interaction

• RE Starting Distribution:– Gaussian, spherically symmetric, radial motion only, and

total energy = He Ground State Energy; available KE is randomly distributed between electrons

– We allow system to propagate without any laser field for time of 1 laser cycle (~100 a.u.).

• Resulting distribution is basically independent of details of initial radial distribution

We use a 10-cycle trapezoidal pulse (2+6+2), polarized in z direction;

=780 nm (16-photon single ionization, 50 double)

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−2 /r→ −2 / r2 + 0.8252

Final momenta parallel to laser polarization for ionized electron pairs

• Population in quadrants 2 and 4 indicates emission into opposite momentum hemispheres

• Having population in all 4 quadrants is consistent with experiment (e.g., V.L.B. de Jesus, et al., Journal of Electron Spectroscopy 141, 127 (2004)).

I=.2 PW/cm2 I=.4 PW/cm2

I=.6 PW/cm2 I=.8 PW/cm2

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 escape nuclear well.

Delay time between recollision & double ionization

• Most DI trajectories show a part-cycle phase delay between recollision and double ionization

Final momenta sorted by: delay times from recollision to ionization

and by final direction relative to recollision direction

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delay<1/25 cycle delay<1/4 cycle

delay<1/2 cycle delay≥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 final z- momenta are opposite from the recollision direction.

•With increased delay times, there is increased spillover into the 2nd and 4th quadrants.

I=6x1014 W/cm2

So…

Q: When in the laser cycle do the recollisions and ionizations typically occur?– Recollision model: The most energetic

recollision events occur just before a laser zero

– [e.g. Corkum 71, 1994 (1993)]

– Ionization: The confining potential-energy barrier is most suppressed when the field is maximal a quarter cycle later

When in laser cycle do recollisions and ionizations occur?

Background curve shows laser cycle.

Red--double ionization within 1/2 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 > 1/2 cycle).

• Collisions peak just before a zero of the laser.

• But Ionizations peak just before the laser reaches full strength.

Classical 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 momentum immediately after collision and are pushed back opposite from the recollision direction

• Direction change after collision the maximum drift momentum for either electron is (2Up)1/2

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Sample has I =4x1014 W/cm2

Classical 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 momentum immediately after collision and are pushed back opposite from the recollision direction

• Direction change after collision the maximum drift momentum for either electron is (2Up)1/2

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Sample has I =4x1014 W/cm2

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)

En

erg

y (a

u)

time (cycles)

time lag for this trajectory is 0.18cycle

In most cases there is a time lag between recollision and the ionization of the second electron

time lag for this trajectory is 0.18cycle

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Energy diagram (shows z only)

Here’s an example with a slightly longer time lag

time lag for this trajectory is 0.22 cycle

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• If, to first approximation, second electron ionizes after the field peaks, the electrons can have drift velocities in opposite momentum hemispheres.

And, finally, sometimes the phase delay between recollision and ionization is > half a cycle. In that case the field ionization of the second electron is basically uncorrelated with the drift direction of the first.

Other notes *Electron exchange occurs in about 1/3 the recollisions *Recolliding electron often misses on first return

Conclusions so far:

• The 3D ensemble method predicts population distributions in semi-quantitative agreement with experiment;

• The method indicates that there is typically a phase delay between recollision and double ionization

and this phase delay is crucial in determining final electron correlations.

• Because of the direction change after recollision, maximum momentum is about (4Up)1/2, maximum energy about 2Up

Preliminary results for =390 nm• Parker et al (PRL 96, 133001 (2006))

considered =390 nm– Total electron pair energy to about 5.3 Up

– Experiment and 3-d quantum theory in agreement

(4Up)1/2

Our results (I=1.1x1015 W/cm2, =390 nm):

5.3Up4Up

I=1.1x1015 W/cm2

I=0.8x1015 W/cm2

Our classical ensemble also gives high-energy (E>2Up; |p|>(4Up)1/2) electrons

Electron momentum distribution,from their paper:

Our result for =390 nm:

Minimum delay of at least 0.2 cycles between recollision and ionization

We can back analyze the trajectories

Energy (au)

prob

den

sity

Final Energies of the two electrons-recolliding (blue) & “struck” (red)

(for trajectories with a high energy electron)

2Up

The high-energy electron is usually the struck electron

For high-energy electrons

Recollision times:

red--final momenta in same hemisphere w/in half cyclegreen--opposite hemisphere w/in half cycleblue--time delay of > 1/2 cycle

Ionization Times:

The production of a high-energy (E>2Up) electron

Conclusions for =390 nm

• Ensemble method gives electrons of energy >2Up

• The higher energy electron is most often the struck electron

• In our ensemble the high-energy electrons result from ionizations that feature the right phase match between motion of the electron in the nuclear well and the laser field