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Recollision, Time Delay, and Double Ionization
studied with 3-D Classical Ensembles
S.L. Haan, A. Karim, and Z. Smith
Calvin College
Grand Rapids MI USA
J.H. Eberly
University of Rochester
Rochester NY USA
Also acknowledging contributions of
C. Cully, A. Vache, D. Tannor, and L. Breen of Calvin College
R. 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
Overview of Method
• 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.
Some Details
– To prevent self-ionization of our starting state, we shield the
electron-nucleus interaction
2/r 2/ r2  0.8252
• 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)
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
I=6x1014 W/cm2
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 zmomenta are opposite
from the recollision
direction.
•With increased delay
times, there is increased
spillover into the 2nd and
4th quadrants.
delay<1/25 cycle
delay<1/4 cycle
QuickTime™ and a
Photo - JPEG decompressor
delay<1/2
cycleto see this picture.delay≥1/2 cycle
are needed
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
Sample has I =4x1014 W/cm2
QuickTime™ and a
Animation decompressor
are needed to see this picture.
• Direction change after collision  the maximum drift
momentum for either electron is (2Up)1/2
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
Sample has I =4x1014 W/cm2
QuickTime™ and a
Animation decompressor
are needed to see this picture.
• Direction change after collision  the maximum drift
momentum for either electron is (2Up)1/2
In most cases there is a time lag between recollision
and the ionization of the second electron
Energy (au)
• 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)
time lag for this trajectory is 0.18cycle
time (cycles)
In most cases there is a time lag between recollision
and the ionization of the second electron
Energy diagram (shows z only)
QuickTime™ and a
Animation decompressor
are needed to see this picture.
QuickTime™ and a
Animation decompressor
are needed to see this picture.
time lag for this trajectory is 0.18cycle
Here’s an example with a slightly longer time lag
QuickTime™ and a
Animation decompressor
are needed to see this picture.
time lag for this trajectory is 0.22 cycle
• If, to first approximation, second electron ionizes after the field
peaks, the electrons can have drift velocities in opposite
momentum hemispheres.
QuickTime™ and a
Animation decompressor
are needed to see this picture.
QuickTime™ and a
Video decompressor
are needed to see this picture.
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
Electron momentum distribution,
from their paper:
– Total electron pair energy to about 5.3 Up
– Experiment and 3-d quantum theory in
agreement
I=0.8x1015 W/cm2
Our results (I=1.1x1015 W/cm2, =390 nm):
I=1.1x1015 W/cm2
Our result for =390 nm:
(4Up)1/2
4Up
5.3Up
Our classical ensemble also gives high-energy (E>2Up; |p|>(4Up)1/2) electrons
We can back analyze the trajectories
Minimum delay of at least 0.2 cycles between recollision and ionization
prob density
Final Energies of the two electronsrecolliding (blue) & “struck” (red)
(for trajectories with a high energy electron)
2Up
Energy (au)
The high-energy electron is usually the
struck electron
For high-energy electrons
Recollision times:
Ionization Times:
red--final momenta in same hemisphere w/in half cycle
green--opposite hemisphere w/in half cycle
blue--time delay of > 1/2 cycle
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
1/--страниц
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