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typical kHz experiment
amptdc
TOF/MS
TMP
TMP
UHV
time
-metal
faraday
photodiode
disc
20
15
10
TW/cm2
xenon, 1m, 30ps
high sensitivity results
photoelectrontotal rate
[o int(t)](t) iħ(t)
TDSE-SAE
10
20
30
TW/cm2
HHG
electrons
helium: kHz experiment
plat du jour: helium & the rebirth of the classical picture
0 100 200 300 400 500
energy (eV)
1E-4
1E-2
1E+0
1E+2
1E+4
1E+6e
co
un
ts
0 2 4 6 8 10 12
E/U p
0.8 m1 PW/cm2
sim
ple
ma
n
time-of-flight (s)
ions
+7
+5
+3+1
argonchargestates
Lompre et al. (Saclay)
wavelength (nm)16 14 1012 8
log(
phot
ons)
H51 H79
photons
High harmonic generationL’Huillier et al. (Lund)
He
800 nm
1.6 eV
Non-linear Non-resonant Non-perturbative
log(
elec
tron
s)
electrons
1 PW/cm2
strong-field atomic physics II
Louis DiMauro
why helium?
largest binding energy (Ip = 24.5 eV) of all neutral atoms
1E+14 1E+15 1E+16
intensity (W/cm 2 )
1E-6
1E-4
1E-2
1E+0
1E+2
1E+4
1E+6
ion
sig
na
l
He+
OTB 1. over-the-barrier (OTB) ionization:Eo = Ip
2/4q3Zhelium: Eo = 0.2 au (1.4 PW/cm2)
2. measurements:Is = 0.8 PW/cm2 (Eo = 0.15 au)
3. Keldysh: = (Ip/2Up)1/2 = 0.49Up = 50 eV @ 0.8 m = 50 au (25Å) ao ~ 1Å
R I3/2
4. theory: He He+ + e
ADKTDSE-SAE
1E+14 1E+15 1E+16
intensity (W/cm 2 )
1E-6
1E-4
1E-2
1E+0
1E+2
1E+4
1E+6
ion
sig
na
l
He+
total rateB. Walker et al., PRL 73, 1227 (1994)
Fie
ld a
mpl
itude
2
Time
electric fieldE = Eo sint
o
velocityv(t) = Eo/[cost - coso] + vo
quiver drift
for tunneling, vo=0
the simpleman’s picture of ionization
quasi-classical description
3 5
Pos
ition
Time
Position
Time
3 5
Pos
ition
Time
Optical Cycles
electron-core interaction ~ ½ cycle electron gains field energy
Posi
tion
collision
21 3
classical model: rescattering
x(t) = Eo/2 (sint - sino + (o - t) cos o)phases collision trajectories
Optical Cycle
simple symmetry argument~ ½ contribute
Schafer, Yang, DiMauro & Kulander PRL 70, 1599 (1993)P. Corkum PRL 71, 1994 (1993)
classical model: rescattering
• 3-step view of quasi-classical rescattering.
r r r
excitationt=0
propagation¼-cycle
rescattering½-cycle
time
classical model: high harmonic connection
800 nm25 fs
1015 W/cm2
HHG
log
(nu
mbe
r of
ph
oto
ns)
helium
16 14 12 10 8
wavelength (nm)
H79H51
table-top source of coherent short wavelength light. potential for generating attosecond (10-18 s) light pulses.
gas jet gas filled capillary
Murnane & KapteynHIGH HARMONIC RADIATION
Helium, 800 nmCutoff ~ 3Up + IP 3Up
classical model: rescattering
0 1 2 3
e return energy (E/Up)
0.25
0.3
0.35
0.4
0.45
0.5
e in
itial
pha
se (
t ) 3.17 U
p cuto
ff
return energy: T(t = tr) = 2Up (cos2 r + cos2 o - 2cos o cos r )
Cutoff rule:3.17Up + Ip
PHYSICAL CONSEQUENCE: electron capture results in odd harmonic photons.
harmonic cutoff: (3Up + IP) rule !!
elastic scattering yields energetic (10Up) electrons.
inelastic e-2e scattering multiple electron ejection.
r r r
excitationt=0
propagation¼-cycle
rescattering½-cycle
time
elastic rescattering
initial bs velocitynormal drift
new elastic cutoff:T = 10Up
0 100 200 300 400 500
energy (eV)
10-10
10-8
10-6
10-4
10-2
100
e co
unts
0 2 4 6 8 10 12
E/U p
He+ - e scattering
quantum model: TDSE-SAEK. Schafer et al. PRL 70, 1599 (1993)
tunnel (vo=0)v(t) = Eo/[cost - coso]
backscatter ( = )set: v(r) = -v(r)
v(t > tr) = Eo/[(cost - cosr) – (cosr - coso)]
elastic rescattering: SFA approximation
0 2 4 6 8 10 12 14
E/Up
-25
-20
-15
-10
-5
0
5
log
rate
fulltunnelfwrdback
Semi-classical solution of generalized SFALewenstein et al., PRA 51, 1495 (1995)
backscattering results in production of high energy electrons
divide optical cycle into a large number of equally spaced time intervals and calculate a tunneling rate.
at each phase of the field, launch a gaussian wave packet at the outer turning point of the suppressed effective potential with zero velocity.
initial conditions are determined from SAE results. propagate in the combined field until it escapes or returns
to the plane of the nucleus. returning trajectories are assumed to spread freely. allow for only one return of the wave packet. calculate the differential elastic cross-section using partial
wave analysis. electron spectrum is determined by summing all time intervals. double ionization is calculated using field-free e-2e inelastic
cross-section. spatial and temporal averaging is included for comparison to
measurement.
rescattering: numerical method (Kulander)
0 100 200 300 400 500
energy (eV)
1E-4
1E-2
1E+0
1E+2
1E+4
1E+6e
co
un
ts0 2 4 6 8 10 12
E/U p
SQC
0 100 200 300 400 500
energy (eV)
1E-4
1E-2
1E+0
1E+2
1E+4
1E+6e
co
un
ts0 2 4 6 8 10 12
E/U p
SQC
Coulombscattering
0 100 200 300 400 500
energy (eV)
1E-4
1E-2
1E+0
1E+2
1E+4
1E+6e
co
un
ts0 2 4 6 8 10 12
E/U p
SQC Coulomb
He+ - e scattering
the short-range physics is important. quantum diffusion reduces the effective rescattering. the recollision occurs in less than an optical cycle.
elastic rescattering: experiment & theory
helium, 0.8 m, 0.8 PW/cm2
elastic rescattering: intensity dependence
Remember, Up Intensity !!
0 100 200 300 400
electron energy (eV)
10-01
1001
1003
1005
elec
tron
cou
nts
0.20.41
PW/cm2
helium, 0.8 m
0 2 4 6 8E/Up
10-8
10-6
10-4
10-2
100
no
rma
lize
d c
ou
nts
in scaled energy, distributions look similar!
elastic rescattering: intensity dependence
2/sin
1
16
1dd
42o
3Up
0 50 100 150 200
Up (eV)
10-8
10-6
10-4
10-2
100
Rutherford (coulomb) scattering
bvo
elastic rescattering: intensity dependence
0 2 4 6 8E/Up
10-8
10-6
10-4
10-2
100
no
rma
lize
d c
ou
nts
not bad for an experimentalist.
Rutherford predicts a 100-fold decrease in high energy electronsover intensity range of experiment.
elastic rescattering: intensity dependence
1014
1015
intensity
10-6
10-5
10-4
10-3
10-2
He: exp
coulomb
e – He+
helium: experiment & theory
0 50 100 150 200 250
0 2 4 6 8 10 12
0 200 400 600 80010
-4
10-2
100
102
104
e co
unts
0 2 4 6 8 10
100 200 300 400 500
0 2 4 6 8 10
energy (eV)
Up
elastic rescattering: atomic dependence
rescattering is sensitive to the atomic core (cross-section).
0 100 200 300 400 500 600 700
energy (eV)
10-4
10-2
100
102
104
106
ele
ctro
n c
ounts
0 2 4 6 8 10 12E/U p
He (expt.)Ne (expt.)1 PW/cm2
1014
1015
10-6
10-5
10-4
10-3
10-2
ele
ctro
n r
atio
(>
2U p
)/(<
2U
p)
He: expNe: exp
coulombe – He+
e – Ne+
intensity (W/cm2)
elastic rescattering: differential cross-section
scattering
bvo
initial bs velocitynormal drift
vx(t) = Eo/[(cost - cosr) – cos (cosr - coso)]
vy(t) = -Eo/[sin (cosr - coso)]
relationship between scattered, , and detected, d, angles.
sin
1coscos
coscot
v
vcot
or
r
y
xd
elastic rescattering: differential cross-section
1 2 3 4 5 6 7 8 9 10
E/Up
80
100
120
140
160
180
dete
ctor
ang
le,
d
electron cutoff energy versus detector angle
90 120 150 180
detector angleA
DK
rat
e
90 120 150 180
detector angle
AD
K r
ate
90 120 150 180
detector angle
AD
K r
ate
8Up6Up2Up
0 100 200 300 400 500
energy (eV)
1E-6
1E-4
1E-2
1E+0
1E+2
1E+4
ele
ctro
n c
ou
nts
0 2 4 6 8 10
E/U p
0102040
elastic rescattering: differential cross-section
helium, 0.8 m, 1 PW/cm2
0 2 4 6 8 10
10-7
10-4
10-1
0 2 4 6 8 10
electron energy, E/U p
10-10
10-7
10-4
10-1
0 20 40 70 90
elec
tron
cou
nts
elastic rescattering: differential cross-section
helium: experiment & theory
)t(i)t()t(into
Ken Kulander
quantum view
time
m/q
• multiple charge states readily observed in an intense laser field.• some charge states cannot be described by a “single” rate.
“direct”ionization
strong-field double ionization
two mechanisms result in the formation of He2+ !!
1E+14 1E+15 1E+16
intensity (W/cm 2 )
1E-6
1E-4
1E-2
1E+0
1E+2
1E+4
1E+6
ion
sig
na
l
He+
He2+
NS
1E+14 1E+15 1E+16
intensity (W/cm 2 )
1E-6
1E-4
1E-2
1E+0
1E+2
1E+4
1E+6
ion
sig
na
l
He+
He2+
NS
He He+ + e
He+ He2+ + e
some insights into double ionization: NS linked to depletion of the neutral ground
state. first electron tunnels into the continuum. the NS yield is strongly polarization dependent
as compared to the sequential processes.
helium double ionization: total rate
we ran out of steam: computationally
tomorrow’s plat du jourtwo-electron soup á la carteexperiments pioneer the future
-1 0 1ellipticity
norm
aliz
ed H
e 2+
yie
ld
-1 0 1ellipticity
norm
aliz
ed H
e+ y
ield
0.2 (NS) and 4 (sequential) PW/cm2
helium double ionization: polarization dependence
In neon, polarization dependence of NS and HHG agreed with classical analysisDietrich et al. PRA 50, R3585 (1994)
1E+14 1E+15 1E+16
intensity (W/cm 2 )
1E-4
1E-3
1E-2
1E-1
He2
+(N
S)
/ H
e+
ratio 3He
4He
• Experiment performed at two intensities.0.8 PW/cm2 1/5000.4 PW/cm2 1/1000
• 3He is used for coincidence measurement.
helium double ionization: high sensitivity
helium double ionization: high sensitivity
1800 “background” electrons2 “signal” electrons
The Needle in the Haystack
helium double ionization: e-ion coincidence
interactionregion
e specmass spec
mechanical referencing design common interaction volume pulsed mode operation dual MCP detection UHV environment (10-10 t)
mass spectrometer electron spectrometer
helium double ionization: e-ion coincidence
e-ion coincidence apparatus: test
an 8:1 Xe:Kr gas mix test was used to test the coincidence apparatus.
0 200 400 600 800 10000
1
2
3
4
5
6
Nor
mal
ized
Cou
nts
Electron Time of Flight (ns)
Regular Xe-Kr Mix Pure Krypton
0 200 400 600 800 1000
Electron Time of Flight (ns)
Kr Coincidence Pure Krypton
T:F ~ 3:1
it really, really works!
He+
He2+
double ionization results in “hotter” distribution than single ionization. distribution consistent with e-2e rescattering.
25 50 75 100 125
3He+
3He2+
Electron Energy (Up)
Electron Energy (eV)
1 2 3 4 5
4×1014 W/cm2
50 100 150 200 250
0.01
0.1
1
10
100
1000
Nor
mal
ized
Cou
nts
/ eV
Electron Energy (eV)
1 2 3 4 5Electron Energy (Up)
8×1014 W/cm2
205M shots45M He hits1058 He2+ coin
helium double ionization: electron distributions
e-2e
Corkum (1993)
release first electron at phase i
if return energy is sufficient to excite second electron to first excited state (40 eV), then proceed.
all excess energy goes to first electron (forward or backward). second electron is then field ionized with zero initial kinetic energy.
1.6 1.8 2.0 2.2 2.40
1
2
3
4
5
6
0
50
100
150
200
250
fina
l ele
ctro
n e
ne
rgy
(U p)
initial phase i (rad)
Backward Zero Forward
en
erg
y (e
V)
8×1014 W/cm2
helium double ionization: classical interpretation
electron energy (Up)
coun
ts (
arb
units
)
100
1
.001
1 2 3 540
backscatteredforward
helium double ionization: S-matrix calculation
shake-off
correlated energy sharing
Frankfurt groupAr2+ & He2+ ion recoil (COLTRIMS)Ar2+ e-ion coincidence
Freiburg groupNe2+ ion recoil (COLTRIMS)Ar2+ e-COLTRIMS
Crete groupXe2+ e-ion coincidence
Michigan groupAr2+ e-ion coincidence
BNL groupAr2+ & Xe2+ e-ion coincidence
double ionization experiments: other atoms
e-2eclassicallyforbidden
0.1 1intensity, PW/cm 2
1E-6
1E-5
1E-4
1E-3
1E-2
ratio
, He2
+/H
e+
10 100
return energy, 3.2U p, eV
NS
The double-to-single ionization ratio is equal for 800 nm & 400 nm excitation.
is everything perfect in the world?
helium, 0.4 m reduce ponderomotive energy by 4 since Up 2