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