photoelectron energy distribution for 1.6 eV photons
xenon at 1014 W/cm2
0 10 20 30 40 50 60
energy (eV)
1E+0
1E+2
1E+4
h
“photon description”
helium at 1015 W/cm2
0 100 200 300 400 500
energy (eV)
1E-4
1E-2
1E+0
1E+2
1E+4
“dc-tunneling picture”
strong-field atomic physics I
Louis DiMauroOSU 2005
• understand the limit where Hint Ho
• probe on a time-scale where t < to
• guide dynamics by tailoring Hint(t)
time-dependent Schrődinger equation
[o int(t)](t) iħ(t)
strong-field atomic physics I
Louis DiMauroOSU 2005
photoelectric effect
electron energyEe = h - ip
transition probability: P = Fwhere cm2, F /cm2 s, s
consider cw-light: = (1A)2 = 10-16 cm2
for P 1: F ~ 1016 /cm2 sor intensity I ~ 10-3 W/cm2
100 fs (10-13 s) light pulse:for P 1: F ~ 1029 /cm2 sor intensity I ~ 1010 W/cm2
h ip
0
Ee
Einstein (1905)
multi-photon photoelectric effect
transition probability: P = a F b F or P = 2 F2 where 2 a b = cm4 s
ip
0
Ee
h
h
electron energyEe = 2h - ip
b
a
2-photon case (h ip)
0
Ee
electron energyEe = nh - ip h ~ 0
ip
transition probability: P = n Fn where n cm2n sn-1
n-photon case (h ip)
Tunnel Rate 1/E eE
+ - + -
x x
V + =
coulomb-1/x
DC fieldxE
Stark-1/x + xE
x
- + - +
x
=
dc field-xE
stark-1/x - xE
x
dc-tunnel ionization
ac-tunnel ionization
electroncurrent
E-field
• electrons are emitted as burst every ½-cycle.
<< 1 tunneling low frequencyand/or high intensity
“dc-tunneling picture”
“photon description”
>> 1 multiphoton high frequencyand/or low intensity
optical frequencytunneling frequency
Keldysh (1964) theory of ionization
+ -r=510-9 cm Coulomb Law
E= q/r2 ~ 5109 V/cm 1au
What laser intensity gives an equivalent field strength?
time
field
am
plitu
de
22pp W/cmcEI 16103
2 o
hydrogen atom
1.06 m, 4 1013 W/cm2
0.53 m, 8 1012 W/cm2
S=0
S=1
Xe: Ip =12.1 eVEe = Nh - Ip
0.53 m, N=6, EN=1.9 eV1.06 m, N=11, EN=0.77 eV
ATI: N+S = (N+S)h - Ip
0.53 m, S=1, E7=4.2 eV
above-threshold ionization (ATI) à la Agostini
think in ponderomotive units !!!
ponderomotive or quiver energy:Up 2 /4
displacement: 2
For 800 nm (red) laser at 1015 W/cm2
Up 60 eV50 au (25 A)
motion of the free electron
0 5 10 15 20 25
energy (eV)
0
ele
ctro
n c
ou
nts
0 2 4 6 8
E/U p• xenon• long pulse, 30 ps • 1 m , 30 TW/cm2
Xe Xe+
ionization energy
h
Xe Xe+
ionization energy +Up(I)
N+S() = (N+S)h - Ip – Up()intensity-dependent energy
ATI & ponderomotive threshold shift
perturbation theoryf()=2n P2n(cos)
electrons are repelled from regions of high intensity.
long pulse (adiabatic)quiver E translational
y
x
ponderomotive acceleration
pUpF
N+S(r,) = (N+S)h - Ip – Up(r,) + Up(r,)intensity-independent energy
Freeman et al. PRL 59, 1092 (1987)
0 1 2 3 4 5
energy (eV)
ele
ctro
n c
ou
nts
5 678 inf 5 678 inf 5 678 inf
Xenon, 100 fs, 800 nm, 70 TW/cm2
short pulse “resonant” ATI
for short pulse the ponderomotive gradient is negligible.
0e
lect
ron
en
erg
y
E0
ele
ctro
n e
ne
rgy
E0
ele
ctro
n e
ne
rgy
EE0
ele
ctro
n e
ne
rgy
I
E
0e
lect
ron
en
erg
y
0 1 2 3 4 5
energy (eV)
ele
ctro
n c
ou
nts
5 678 inf 5 678 inf 5 678 inf
Experiment is a spatial and temporal average of intensity I(r,t).
role of resonance
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:• Gallagher, PRL 61, 2304 (1988)• Van Linden van den Heuvell & Muller, in Multiphoton Processes (1988)• Corkum, Burnett & Brunel, PRL 62, 1259 (1989)
0 1 2
E/Up
elec
tron
cou
nts
v(t) = Eo/[cost - coso] Quiver Drift
V
x
0 1 2
E/Up
elec
tron
cou
nts
V
x Maximum drift energy = 2Up.
0 1 2
E/Up
elec
tron
cou
nts
predictions of the simpleman
0 1 2
E/Up
ele
ctro
n c
ou
nts
Tunnel Rate 1/E eE
in the experiment, we detect the drift energy not quiver !!
T = mv2/2 = 2Up cos2 o
simpleman comparison to experiment 1
0 5 10 15 20 25
energy (eV)
0
ele
ctro
n c
ou
nts
0 2 4 6 8
E/U p
xenon 30 TW/cm2
Up = 3 eVbad news!
helium 1 PW/cm2
Up = 50 eVgood news!
remember Up !!!
simpleman comparison to experiment 2
Agostini, Muller et al.
1s22s22p63s23p6
1s22s22p53s23p6
L-shell ionization
e(200 eV)+ dressing
Simpleman sideband estimate:
v(t) = Eo/[cost - coso] + vo with vo
kinetic energy
oopo2
po cosT2U2)cos2
1(U2TT
broadening:
op T2U2T
experiment:To = 200 eV, Up = 20 meV T = 6 sidebands
good simpleman!
moving beyond the simpleman
quantum model: TDSE-SAEK. Schafer et al. PRL 70, 1599 (1993)
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
~ 10-4–5
helium, 0.8 m, 1 PW/cm2
ideal case 10 Hz & 100 channel experiment:100 e/shot or 1 e/ch*s, 105 range 28 hrs!
1 au field adequate for atomic physics?
n-photon ionization perturbation theory: P = n Fn saturation (depletion): P Fs = (n )-1/n
helium (24 eV, 16-photons):Fs = 1033 p/s*cm2 or Es ~ 0.1 au
over-the-barrier ionizationV(x) = -Ze2/x – eEox
solve for Eo:Eo = Ip
2/4q3Z
helium: Eo = 0.2 au
answer: 1 au field is adequate for neutral atomic ionization!
for high sensitivity measurements
baseline: 1 au field strength (3.5 1016 W/cm2)
pulse: 100 fs duration & 4 m beam waist 1 mJ pulse energy
typical laser produces a few Watts average power 103 pulses per second
kilohertz regenerative amplification (late 1980s):Mourou, Bado, Bouvier (Rochester)Saeed, Kim, DiMauro (BNL)Fayer (Stanford)…
seminal work (LLNL):Lowdermilk & Murray, J App. Phys. 51, 2436 (1980).
for kilohertz regenerative amplification
cw or quasi-cw pumpingfactors: absorption spectrum, lifetime, thermal coefficients, …
material propertiesdamage, saturation fluence, …
YLF, YAG, glass: millisecond lifetimes, broad absorptionpoor thermal properties, narrow emission
Ti:sapphire: microsecond lifetimes, narrow absorptiongood thermal properties, broad emission
advantages of regenerative amplification:high amplification 106-8
excellent spatial modegood stability 1-3% rms
kHz regenerative amp circa MDCCCCLXXXVIII AD
HR
HR
Pockels cellYLF head
coupling polarizers
PD1
PD1Q-switch & trapPD1dump
out
• extract maximum energy• minimize optical damage
1000xstretcher
positiveGVD
amplifiermedia
ultra-fastlaser
oscillator
* G. Mourou and Strickland (1985)
Chirped Pulse Amplification (CPA)
1000xcompressor
negativeGVD
state-of-the-art systems 1020 W/cm2
kilohertz operation 1016 W/cm2
for amplifying short pulse
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
0 5 10 15 20 25 30 35 40
energy (eV)
100
102
104
ele
ctr
on
co
un
ts
0 2 4 6 8 10 12
E/U p
higher sensitivity new insights
scattering “rings” in high-order ATI
xenon, 1 m, 1013 W/cm2
0 5 10 15 20 25 30 35
ATI order
0
15
30
45
30 TW/cm^2
1/2
“rings” appear within an energy window !
0 5 10 15 20 25 30 35
ATI order
0
15
30
45
19 25 30 TW/cm^2
“rings” appearance is intensity dependent! “rings” scale with ponderomotive energy
• Remember, Up Intensity !!
0 2 4 6 8 10 12 14
E/Up
0
15
30
45
19 25 30 TW/cm^2
0 2 4 6 8 10 12 14
E/Up
0
15
30
45
19 25 30 TW/cm^2
0 2 4 6 8 10 12 14
0
20
40
60
80
theory: Schafer & Kulander
scattering “rings”: intensity dependence
scattering “rings”: short pulse
xenon, 0.8 m, 50 fs
exp 1D
argon, 0.8 m, 50 fs
1D: soft core potential: V(x) = -(1 + x2)-1/2
helium: kHz experiment
tomorrow’s 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