Attosecond Flashes of Light

– Illuminating electronic quantum dynamics –

XXIIIrd Heidelberg Graduate DaysLecture Series

Thomas PfeiferInterAtto Research GroupMPI – Kernphysik, Heidelberg

Fourier Transform

Contents

Basics of short pulses and general concepts

Attosecond pulse generationMechanics of Electrons

single electronsin strong laser fields

Attosecond Experiments with isolated Atoms

Multi-Particle SystemsMoleculesmulti-electron dynamics (correlation)

Attosecond experiments with molecules / multiple electrons

Ultrafast Quantum Controlof electrons, atoms, molecules

Novel Directions/ApplicationsTechnology

Mathematics of Ultrashort pulsesspectral phaseTaylor expansiondispersion

absolute (carrier-envelope) phase

Windowed Fourier Transform

freq

uenc

y [a

rb. u

.]

frequency [arb. u.]

‘Gabor Transform’

Contents

Basics of short pulses and general concepts

Attosecond pulse generationMechanics of Electrons

single electronsin strong laser fields

Attosecond Experiments with isolated Atoms

Multi-Particle SystemsMoleculesmulti-electron dynamics (correlation)

Attosecond experiments with molecules / multiple electrons

Ultrafast Quantum Controlof electrons, atoms, molecules

Novel Directions/ApplicationsTechnology

Ultrashort Pulses

1000000000000000

power = work

time

Observation of fast processes concentration of energy in time and space

1 fs = 10-15

s

Ref: Ulrich Weichmann, Department of Physics, Wuerzburg University

Short Pulses Intense Laser Fields

femtosecondlaser pulse

Plasma

e-

e- e-e-

X+

e-

X+

X+ X+X+

Power = EnergyTime

100 J5 fs

= = 20 GW

20 GW(100 m)2

= 2 1016 Wcm2

relativistic effects above 1018W/cm2

Supercontinuum generation

Attosecond pulse generation

detector/experiment

atomic medium

femtosecondlaser pulse

also known as: High-Order Harmonic Generation

laser intensity:>1014 W/cm2

attosecondx-ray pulse

mechanism based on:sub-optical-cycle electron acceleration

(laboratory-scale table-top)

High-(order) harmonic generationfirst signs

McPherson et al. J. Opt. Soc. Am. B 21, 595 (1987)intensity: 1015-1016 W/cm2

wavelength: 248 nmpulse duration: 1 ps

High-(order) harmonic generationfirst signsM. Ferray, A. L’Huillier et al. J. Phys. B 21, L31 (1988)

intensity: ~1013 W/cm2

wavelength: 1064 nmpulse duration: 1 ps

in Xenon (Xe)H3

H5H7H9H11

H15

H13

80 fs800 nm5·1014 W/cm2

1 kHz

Zr + Parylene-N filter

in Neon (Ne)

80 fs800 nm3·1014 W/cm2

1 kHz

High-harmonic generation (HHG)

Contents TodayAttosecond Pulses

Classical and quantum mechanics of electronsand experiments with isolated atoms

- Classical Motion of Electronsdefinition of important quantities

- Quantum Mechanics· Electron dynamics in (intense) laser fields· Ionization

- High-harmonic generation: quantum mechanical view

- Experiments with attosecond Pulses

- Quantum state interferometry

Forces on Electrons in Atoms

e-F

E(t)Intensity I ~ 1015 W/cm2

Force F = 14 nNMass me= 9.1∙10-31 kgacc. a = 1.5∙1022 m/s2

velocity v = 3 ∙106 m/s = 1% c (speed of light)

“assumed constant acceleration from restfor 200 attoseconds”

2000 as

optical light wave

E(t)

1 attosecond (1 as = 10-18 s) compares to 1 secondas 1 second compares to more than the age of the universe (~15 Billion years)

Electron in Laser Field

E(t)=E0cos(t)

a(t)= -eE0cos(t)

v(t)= - sin(t)eE0

x(t)= cos(t)eE0

linearly polarized along x axis

acceleration

velocity (dt a)

position (dt v)

ponderomotive potential

ponderomotive radius

Up=Ekin,av= e2E0

2

4m

ap= x0 = eE0

= I29.33 eVm1014 W/cm2

High-(order) harmonic generationfirst signsM. Ferray, A. L’Huillier et al. J. Phys. B 21, L31 (1988)

intensity: ~1013 W/cm2

wavelength: 1064 nmpulse duration: 1 ps

Three-step model

P. Corkum, Phys. Rev. Lett. 71, 1994 (1993)Kulander et al. Proc. SILAP, 95 (1993)

High-harmonic generation (HHG)

High-(order) harmonic generationfirst signsM. Ferray, A. L’Huillier et al. J. Phys. B 21, L31 (1988)

intensity: ~1013 W/cm2

wavelength: 1064 nmpulse duration: 1 ps

H3

H5H7H9H11

H15

H13

High-harmonic generation

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

Hentschel et al. (Krausz group) Nature 414, 509 (2001)

Isolated Attosecond-pulse production

high-passfilter

(the conventional method)

Hentschel et al. (Krausz group) Nature 414, 509 (2001)

“cos pulse”

“sin pulse”

Attosecond pulse generation

Hentschel et al. Nature 414, 509 (2001)

Absolute Phase (CEP) effects

5 10 15 20 25 30 35 400.0

0.1

0.2

0.3

0.4

0.5

0.6

Tra

nsm

issi

on

wavelength [nm]

400 nm Al 400 nm Zr

CEP CEP

~ 6 femtosecond CEP (Absolute phase) stabilized laser pulse

Baltuška et al. Nature 421, 611 (2003)

10 11 12 13 14 150

200

400

600

800120 110 100 90

photon energy [eV]

HH77spe

ctra

l in

ten

sity

[a

rb.u

.]

wavelength [nm]

HH51

Attosecond Beamline at Berkeley

6-fs IR pulseCEP stabilized

Iris

Splitmirror

Filter onpellicle

CCD

Metalfilter

XUV grating

X-rayCCD

High-harmonicgeneration

Velocity-Map imagingof electrons or ions

piezoMCP

Piezo-controlledsplit mirror

Time-of-Flight Detectionof electrons

Attosecond Beamline at Berkeley

Mo/Si multilayer mirror

86 88 90 92 94 96 98 1000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.855 57 59 61 63

Harmonic order (800 nm fundamental)

p-polarized

s-polarized

Ref

lect

ivity

photon energy (eV)

86 88 90 92 94 96 98 1000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.855 57 59 61 63

Harmonic order (800 nm fundamental)

Ref

lect

ivity

photon energy (eV)86 88 90 92 94 96 98 100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.855 57 59 61 63

Harmonic order (800 nm fundamental)

10 Layers

20 Layers

40 Layers

Ref

lect

ivity

photon energy (eV)

6-fs IR pulseCEP stabilized

Iris

Splitmirror

Filter onpellicle

CCD

Metalfilter

XUV grating

X-rayCCD

High-harmonicgeneration

Velocity-Map imagingof electrons or ions

piezoMCP

Piezo-controlledsplit mirror

Time-of-Flight Detectionof electrons

Attosecond Beamline at Berkeley

Short pulse measurement“to measure a fast event, you need an at least equally fast probe”

- Autocorrelation‘Auto...’ -> self...

- Frequency-Resolved Optical GatingFROG, building upon Autocorrelation

- Temporal Analysis by Dispersing a Pair Of Light Electric FieldsTADPOLE

- Spectral Interferometry for Direct Electric Field ReconstructionSPIDER, building upon TADPOLE

linear (no crystal)

nonlinear (with crystal)

Autocorrelation

Attosecond autocorrelation measurementsTzallas et al.(Witte, Tsakiris)Nature 426, 267 (2003)

Attosecond autocorrelation measurementsisolated pulses

Sekikawa et al.(Watanabe)Nature 432, 605 (2004)

Attosecond autocorrelation measurementspulse trains

Tzallas et al.(Witte, Tsakiris)Nature 426, 267 (2003)

FROG idea

Ref: http://www.physics.gatech.edu/frog/

measure spectrum asa function of time delay

2-dim. data sets: ‘FROG-trace’

analysis by iterative algorithm

D. J. Kane and R. Trebino, Opt. Lett. 18, 823 (1993)

Streaking

Goulielmakis et al. (Krausz group), Science 305, 1267 (2004)

FROG-CRABY. Mairesse and F. Quéré, Science 71, 011401 (2005)

high-harmonic generationintense laser field acting on single atom

probability distribution p(x,y)=|(x,y)|2 for the electronic wavefunction

laser polarization

Time-dependent quantum mechanics

n

nnn ttitat )(exp)()(

)()( tHtdt

di

/E

E

dt

d

Time-dependent quantum mechanicsposition and momentum space representation

),(exp),(),( ttitat rkrrr

),(~exp),(~),(

~tititat pr

ppp

~~ ~

Wave packets

Coherence

Also for Quantum wavepackets

Quantum “Motion”

Wave packets

Ionization

Strong electric field(Tunneling)

Photoelectric effect(direct transition)

1st order perturbation theory

t

tietEtdta )(1

10)(~)(

|1>

|0>

tunneling rate

ttEmU

tEw

c etda))((2

))((

~

w: barrier width

U: barrier height

Electron in Laser Field

E(t)=E0cos(t)

a(t)= -eE0cos(t)

v(t)= - sin(t)eE0

x(t)= cos(t)eE0

linearly polarized along x axis

acceleration

velocity (dt a)

position (dt v)

ponderomotive potential

ponderomotive radius

Up=Ekin,av= e2E0

2

4m

ap= x0 = eE0

= I29.33 eVm1014 W/cm2

Electron in Laser Field

E(t)=E0cos(t)

a(t)= -eE0cos(t)

v(t)= - sin(t)eE0

linearly polarized along x axis

acceleration

velocity (dt a)

Vector potential (Coulomb gauge) A(t)= -e dt’ E(t’) = v(t)

-

t

Schrödinger equation: (dipole approximation)

m

teApΗ

ti

2

))((ˆ2

)(2

ˆ2

terEm

pΗ

ti length gauge

momentum/velocitygauge

Electron in Laser Field

E(t)=E0cos(t)

a(t)= -eE0cos(t)

v(t)= - sin(t)eE0

linearly polarized along x axis

acceleration

velocity (dt a)

Vector potential (Coulomb gauge,

A=0)

A(t)= -e dt’ E(t’) = v(t)-

t

Schrödinger equation: (dipole approximation)

m

teApΗ

ti

2

))((ˆ2

momentum/velocitygauge

[H,p]=0 p conserved, solution: )(~)(exp)(~),(~

ppp ttiat

t

tdm

tett

2

)(1)(

2Ap

Keldysh formalism

Photoelectric effect(direct transition)

1st order perturbation theory

t

tietEtdta )(1

10)(~)(

|1>

|0>

Strong electric field(Tunneling)

tunneling rate

ttEmU

tEw

c etda))((2

))((

~

w: barrier width

U: barrier height

p

p

U

I

2 11

t

tin etEtdta )(1

10)(~)(

ADK formulaAmmosov, Delone, and Krainov, Sov. Phys. JETP 64, 1191 (1986)

Experimental checks: Augst et al., J. Opt. Soc. Am. B 8, 858 (1991)

Ionization rate (in a.u.):

Strong electric field(Tunneling)

tunneling rate

ttEmU

tEw

c etda))((2

))((

~

w: barrier width

U: barrier height

1

Keldysh formalism

tunneling rate

Strong electric field(Tunneling)

ttEmU

tEw

c etda))((2

))((

~

w: barrier width

U: barrier height

Strong-Field Approximation

Strong electric field

e-

V(t)=rE(t)

V

r

)()(2

1ˆ 2 trErVpm

Ηt

i

m

teApΗ

ti

2

))((ˆ2

)(~)(exp)(~),(~

ppp ttiat

t

tdm

tetSt

2

)(1)()(

2Ap

High Harmonics Quantum Mechanical

t

t

tdm

tAepttpS ~

2

)~(1),,(

2

high-harmonic generationintense laser field acting on single atom

probability distribution p(x,y)=|(x,y)|2 for the electronic wavefunction

laser polarization

Wavepacket spreading