Atoms in strong laser fields

Johan Mauritsson

Laser – matter interaction

Atoms

Electrons Ions

Photons

Laser – matter interaction Ion detector

+Vacc

Ground

Field-free Flight tube

Detector

Laser – matter interaction Electron or ion detector

Eppink and Parker, Rev. Sci. Instr., 68, 3477 (1997) Vrakking, Rev. Sci. Instrum., 72, 4084 (2001)

Extraction

Detection

Electrons

Ions

2D projection

3D reconstruction

Velocity Map Imaging Spectrometer (VMIS)

- Velocity Map Imaging Spectrometer

ATI in Argon

Excitation vs. ionization

g

f

Igef ∝2

rE

g

Ige ∝2

rEε

ε

2

21 mvE

E

kin

kin

=

+= φωPhotoelectric effect

Selection rules

onpolarizaticircular 1onpolarizatilinear 0

1

±=∆=∆±=∆

mml

s

p

p

s d

Helium Argon

Spherical harmonics (Ylm) and angular distributions

( )

φ

φ

φ

θπ

θθπ

θπ

θπ

θπ

π

i

i

i

e

e

e

222,2

1,2

20,2

1,0

0,1

0,0

sin3215Y

cossin818Y

1cos316

5Y

sin83Y

cos43Y

41Y

±±

±±

±±

⋅=

⋅=

−=

⋅=

=

=

θ0=l

1=l

2=l

0=m

0=m

0=m

1=m

1=m 2=m

Helium ionized by a short XUV pulse

Dye lasers

Ti:sapphire lasers

High-order harmonics

100 as

1 fs

10 fs

100 fs

1 ps

10 ps

1970 1980 1990 2000

Puls

e du

ratio

n

Wavelength > 1 fs

Femtosecond barrier

LASERS Shorter pulses and higher intensities

LASERS Shorter pulses and higher intensities

Inte

nsity

W/c

m2

1010

1015

1020

1025

Q-switching

Mode-locking

CPA

1970 1980 1990 2000

Multi-photon ionization

g

f

22Igeiief ∝rErE

i

(this should actually be a sum over all possible intermediate states)

??? 4 pkin IE −= ω

ATI

First ATI

(1979)

Free electron in laser field

0=kinE 0=kinE???=kinE

I II III

Wiggle energy Ponderomotive energy

What is the energy of an electron wiggeling in a laser field?

Wiggle energy

( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( )

( ) ( ) 2

20

22

2

20

22

P

0

0

0

4cos

221 U :Energy

cos1 :Velocity

sin :onAccelerati

:Force

sin :fieldLaser

ωεω

ωε

ωω

ε

ωε

ωε

met

metvm

tme

tmetE

meta

tmateEtF

ttE

===

−=−=

=−=

=

Suppression of low-energy ATI peaks

Intensity

Ener

gy

-Ip

0

kinEkinE

???

Short vs. long pulses

m 1 µ~

1. The electron has time to leave the focal volume before the laser pulse has passed 2. The electron does not have time to leave the focal volume before the laser pulse has passed

Ponderomotive shift long pulse

I=2.2 1012 W/cm2

I=1.1 1013 W/cm2

Intensity

Ener

gy

-Ip

0

kinE

Ponderomotive shift short pulse

100 0

Phot

oele

ctro

n en

ergy

IR-Harmonic delay (fs) 200

Intensity

Ener

gy

-Ip

0

kinE

Tunnel ionization The strength of the laser is comparable to the intra atomic forces

Tunneling wave packets

• Born near the peak of the IR cycle • Born outside potential well • Initial velocity ~ 0 • Temporal width depends on IR intensity • Periodic process

Repetition of the process

The ionization is maximized every time the laser field is maximized, i.e. twice per laser cycle

Electron “born” in a laser field The final electron energy depends on when during

the laser cycle the electron is ionized

( ) ( ) ( ) ( )

( ) ( )

( ) ( ) ( )[ ]

( ) ( )[ ]( ) ( )[ ]

( )

( ) ( ) PdriftTT

drift

UEtm

em

tvmE

tette

tte

ttet

tedtdtF

tttEttE

+≡+==

−=−=

−=

+−−

=

−==

∂∂

−==

222

2

0

00

000

0

0

222

coscos

coscos

sin

,sin

Ap

ApAA

pp

p

A

ωωωε

ωωω

ε

ωε

ωε

Electron trajectories

Electron trajectories

pdrift

( ) ( )tet drift App −=

Linear vs. circular polarization

Linear vs. circular polarization

Linear vs. circular polarization

( ) ( ) ( )[ ]

( ) ( ) ( )[ ]

PdriftP UEU

tytxt

tytxt

22

2

20

20

12

12

sinˆcosˆ1

cosˆsinˆ1

ξξξ

ωξωξω

ε

ωξωξ

ε

+≤≤

+

++

=

−+

=

A

E

Pdrift

Pdrift

UEUE

=

≤≤ 20Linear:

Circular:

Expected results Above threshold ionization Double ionization

2 Up

He+

He2+

Num

ber o

f ele

ctro

ns

Num

ber o

f ion

s

Intensity

Photoelectron energy

Obtained results Above threshold ionization

2 Up

Num

ber o

f ele

ctro

ns

Photoelectron energy

Double ionization

He+

Num

ber o

f ion

s

Intensity

He2+

10 Up

Obtained results Photons: odd harmonics detected

An extended plateau

Three puzzling observations

• High energy ATI (up to 10 UP) • Double ionization at low intensities • High-order harmonics

III The electron interacts with the atom and: - rescatter - knock a second electron out - emit accumulated energy as a photon

II The free electron is accelerated by the field, and may return to the atomic core

The electron tunnels through the distorted Coulomb barrier I

Three step model

Corkum Phys. Rev. Lett. 71, 1994 (1993)

Schafer et al. Phys. Rev. Lett. 70, 1599 (1993)

The same model can be used to explain all three observation

High kinetic energy electrons

Non-sequential ionization

High-order harmonic generation

High energy ATI

Above threshold ionization

2 Up

Num

ber o

f ele

ctro

ns

10 Up

An electron that scatters and changes direction 180 degrees can pick up additional energy during the next half-cycle.

Rescattered electrons

Non-sequential ionization

He

He+

He++

Electron dynamics in a laser field

Elec

tric

fiel

d

-1

0

1

Time (IR cycles) 0 1 2

Electron trajectories

- Generation of attosecond pulses

Photon emission - an interference effect

Same electron!

Interference leads to an oscillating dipole i.e. photon emission

High-Order Harmonic Generation

Electron dynamics The return energy depends on the time of ionization. Emax(electron)=3.17 UP Emax(photon)=IP+3.17 UP

Atom

Field Electrons

APT – mode locked fs laser analogy

Time

Frequency

Plateau

Cut-off

Single harmonic ~ few fs

~ fs

~as

Several synchronized harmonics ~ few as Two attosecond pulses per IR cycle

Why only odd harmonics? Both odd and even ATI peaks!

Frequency

Time Time

Frequency

Can we generate only one pulse per IR cycle?

Break the symmetry and change the periodicity

Strong IR

M. D. Perry et al., Phys. Rev. A 48, R4051 (1993) H. Eichmann et al., Phys. Rev. A 51, R3414 (1995) I. J. Kim et al., Phys. Rev. Lett. 94, 243901 (2005)

Ionization at these times leads to the same

electron trajectories

Ionization at these times leads to different

electron trajectories

+ =

X momentum

Y m

omen

tum

Angular distributions, single pulse Helium

Pola

rizat

ion

dire

ctio

n θ Momentum

An electron in a strong IR laser field

Itatani et al., Phys. Rev. Lett. 88, 173903 (2002)

∆p=-eA(t)

The quantum stroboscope

Conventional stroboscope: n scaling Quantum stroboscope: n2 scaling + interference

- To increase the signal strength

The quantum stroboscope - Argon and a laser field

Movie