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