Time and space resolved imaging of electron tunneling from molecules.

Time and space resolved imaging

of electron tunneling

from molecules

Olga Smirnova, Max-Born Institute, Berlin

Serguei Patchkovskii, NRC, Ottawa

Misha Ivanov, Imperial College, London

Yann Mairesse, CELIA, Université Bordeaux I

Nirit Dudovich, Weizmann Institute, Rehovot

David Villeneuve, NRC, Ottawa

Paul Corkum, NRC, Ottawa

Strong Field Ionization: Optical Tunneling

V(x)+xE cost

Field free atom/molecule

Tunnel ionization in strong laser fields

• We can remove an electron from different orbitals

• Ion can be left in excited states

Many electrons and multiple orbitals

Ion Ion*

Ionization from molecules

HOMO-1

HOMO-2

Tunnel ionization is exponentially sensitive to Ip

)2(2exp~

X 2g~A 2u~

Ip~13.8 eV

4.3eV3.5 eV

There is more to ionization than IThere is more to ionization than Ipp

Ionization from different orbitals: leaving the ion in excited states

HOMO-1

HOMO-2

Our calculations show that 3 channels are important in CO2

X 2g~A 2u~

Ip~13.8 eV

4.3eV3.5 eV

Multiple ionization channels are important in molecules

Key reasons: Proximity of electronic states in the ion

Geometry of Dyson orbitals

Main message

1. Channel coupling during ionization (laser-induced)

2. Interaction between the departing electron and hole

Main message

1. Affects ionization rates into each channel

2. 2. New parameter: phasephase between channels

Reflected in the shape and location of the hole, its recoil from the electron during ionization

Main message

1. Affects the magnitude of each channel

2. 2. New parameter: phasephase between channels

Reflected in the shape and location of the hole, its recoil from the electron during ionization

How can we image the hole dynamics during tunneling?

Can we measure the phase of ionization?

Consider CO2

HOMO-1

HOMO-2

X 2g~A 2u~

Ip~13.8 eV

Interference suppression of SF ionization

A. Becker et al, 2000, C.D. Lin et al 2002

Suppression at both 0o and 90o

Angular dependence: channel X, I=2.1014 W/cm2

|aT|2=4.5 10-3

Interference suppression of SF ionization

A. Becker et al, 2000

Suppression at both 0o and 90o

X 2g~A 2u~ B 2

HOMO-1

HOMO-2+ -

3.5 eV

Ionization: channel A, I=2.1014 W/cm2

|aA|2=9 10-5= |aX|2/50

θ=90o: |aA|2/|aX|2=1/5

Suppression at 0o

HOMO-1

HOMO-2 + -X 2g~A 2u~ B 2

Ionization: channel , I=2.1014 W/cm2

|aX|2/128|aB|2=3.5 10-5=

|aB|2/|aX|2=1/28Suppression at 90o

Ionization: intermediate conclusions

•Strong-field ionization almost always creates dynamics in the ion (Not specific for CO2)

•This dynamics is different for different orientations of the molecule with respect to the laser field

Visualization of hole dynamics X,A channels~ ~

X,B channels~ ~

• Visualization of hole dynamics for

|X-B|2~ ~

Where does the hole begin its motion after tunnel ionization, and how does it move?

We need to record relative phase between different channels

Direction of tunneling

X,B channels~ ~

|X+B|2~~

|X-iB|2~ ~x

High harmonic spectroscopy

3. Recombination

1. Ionization

2. Propagation

Same initial and final states: ground state of the neutral

Multiple channels in HHG

Different ionization channels-Different ionization channels-different HHG channelsdifferent HHG channels

Ion Ion*

Interference records relative phase between the channels by mapping it into harmonic amplitude

modulations!

High harmonics: temporal resolution

Atto-second temporal resolutionAtto-second temporal resolution

t - time delay between ionization and recombination

N2Ee(t)+Ip

0 2.7 t,fs

~e.g. 60 eV

2fs/20 odd harmonics~100 asec

Each harmonic takes snapshot of the system at a

particular time delay between ionization and recombination

M. Lein,

S. Baker et al

Getting initial phase

BTotal

Destructive interference at XB(*)=(2n+1)

XB(=0)= rec+ion

XB=(EX-EB) + rec+ion

Dynamical minimum is tied to *, not

harmonic number!

I=1.1*1014W/cm2

Amplitude Minima in CO2

I=2.0*1014W/cm2

Minimum shifts with intensity

It is a signature of dynamical minimum and channel interference

H31H25

800nm 40fs800nm 40fs

Intensity dependence of the dynamical minimum

=1.17±0.1fs

1.1014

2.1014

3.1014

Delay , fs Laser Intensity, 1014 W/cm2H

ber cos4()

cos6()

N*= Ee()+Ip

N*∞ (1.7±0.2)Up

Theory vs experiment

Laser Intensity, 1014 W/cm2

cos4()cos6()cos4()cos6()

Experiment: Yann Mairesse, Nirit Dudovich, David Villeneuve, Paul Corkum

cos4()cos6()cos4()cos6()cos4()cos6()exp

The harmonic movie decoded

• Visualization of hole dynamics for aligned CO2:X,B channels~ ~

• In tunneling regime, the initial phase between and is zero, see frame 1: maximum extension in the direction of tunneling.

|X+B|2~~

|X-iB|2~ ~

|X-B|2~ ~

Hole delocalization in multiphoton regime?

3Multiphoton regime

|X-B|2~~

|X-iB|2~ ~

|X+iB|2~ ~

Tracking hole dynamics at longer wavelength

Each harmonic is a frame of an “attosecond movie” (M. Lein; S. Baker et al)

Longer wavelength - longer movie (~),

more frames per fs (~)

=1200nm

X,A channels~ ~

Mapping the period of hole motion

One can monitor separately the length of the period of hole motion and initial phase for each intensity.

X,A channels~ ~

Mapping the period of hole motion

One can monitor separately the length of the period of hole motion and initial phase for each intensity.

X,B channels

Constructive

Destructive

Conclusions

New questions for theory and experiment:New questions for theory and experiment:

• Channel coupling during strong-field ionization

• Relative phase of strong-field ionization between channels, in tunneling and multi-photon regimes.

In simple terms:In simple terms:

• How does the hole recoil from the departing electron?

• How does the hole left in the ion records attosecond dynamics of core re-arrangement during strong field ionization?

Dynamical origin of the minimum

=1.17±0.1fs

N= Ee()+Ip

Up=E2L/42

N∞ (1.7±0.2)Up

=1.8 fs

1.1014

2.1014

3.1014

Delay , fs

N= Ee()+Ip

Up=E2L/42

N∞ 3.17Up

ber cos4()

cos6()

HHG – multichannel interference

Neutral

Interference records relative phase between the channels by mapping it into harmonic amplitude

modulations

Amplitude Minima in CO2, cut of the spectrum for =0o

I=1.1 1014W/cm2

Harmonic number

Interplay of the channels depends on intensity

dominates for high harmonics, dominates for low harmonics

X~ Total Total

800nm 40fs800nm 40fs

Harmonic number

I=2.0*1014W/cm2

HH spectroscopy: the promise (?)

dtetN tiN )(D)(E

Temporal and spatial information about • electron density in the neutral • electron density in the ion• continuum electron: scattering phase

cctttt CONTNION

NNEUT )()(A|d|)()(D )1()(

HHG Observables • photon energy• harmonic amplitude (intensity)• harmonic phase• harmonic polarization

Temporal and spatial information- how it is encoded?

)12(cos

NpIN p

M. Lein et al, 2002

Potential to obtain structural information

- gerade

- ungerade

Structure –related interference minima in HHG

M. Lein et al, 2002, 2D H2+

HHG spectroscopy: spatial resolution

Example: HHG in CO2

Kanai et al, Nature 435, 2005

minimum2cos pR

NB: Molecules are pre-aligned for HHG experiments!

CO2 is different in Tokyo and Milano

Harmonic number

2cos)( RNp

25-27C. Vozzi, PRL 95, 153902 (2005)

Tokyo Milano

CO2 is different in Tokyo and Milano

Harmonic number

2cos)( RNp

25-27C. Vozzi, PRL 95, 153902 (2005)

Tokyo Milano

Ottawa: Mairesse, Dudovich, Villeneuve, Corkum –

The minimum shifts with intensity

> 2. 10 14 W/cm2< 2.10 14 W/cm2

Main message

Theory and Experiment in CO2

•HHG spectra for molecules reflect the contribution of different electronic states of the ion

•The positions of minima in HHG spectrum are related to

•Structure: geometry of participating Dyson orbitals

•Dynamics: the interplay of different states of the ion

•How to tell them apart?

•What can we learn from positions of dynamical minima?

•This dynamics can be further modified by the laser field (Not the case for CO2 in IR field)

•This dynamics is reflected in HHG spectra and we shall see how X, A channels~ ~

X,B channels~ ~

Amplitude minima in harmonic spectra

@ N. Rerikh

3Multiphoton regime

|X-B|2~~

|X-iB|2~ ~

|X+iB|2~ ~

Low intensity measurement (multiphoton regime) is consistent with maximum delocalization

I=1.7*1014 W/cm2I=1.26*1014 W/cm2

Theory vs experiment: HHG spectra

Alignment angle-50 0 50

Alignment angle-50 0 5017 25 31 37

nsity -6

17 21 25 29 33

nsity -6

17 21 25 29

nsity -6

17 21 25 29 37

nsity -6

Alignment angle-50 0 50

I~1.0*1014 W/cm2 I~1.8*1014 W/cm2

Conclusions

• There are several HHG channels in CO2 molecule

• Interference between the channels records attosecond dynamics of ionic states

• Dynamical minimum is tied to recombination time and is strongly dependent on intensity

• Structural minimum is tied to electron energy and is intensity-independent.

• The comparison of theory and experiment has allowed us to ask and answer fundamental question: Where is the hole created and how does it recoil from the departing electron?

Harmonic phases near dynamical minimum

Structural minimum: -phase jumps

Dynamical minimum:

Ab-initio, 2D H2+, Lein et al, 2002

phase jumps near dynamical minima

I=2.0*1014W/cm2

Molecular alignment angle,

Harmonic Phase, units of

I=2.0*1014W/cm2

I=1.3*1014W/cm2

Intensity dependence of the phase

Circular dichroism

|ER|2- |EL|2

|ER|2+ |EL|2=

Circular dichroism means that system responds differently to left and right circularly

polarized light:

no left-right symmetry

Circular dichroism of harmonic emission: why?

1. Anisotropy of molecular potential: returning electron does not have to move along the field

Elaser

Circular dichroism of harmonic emission: how?

ElaserHHG||HHG┴

Laser field dominates the motion of continuum

electron and HHG┴<<HHG||

Conditions of high circularity:

1. Suppress HHG|| -> HHG||~ HHG┴

. /2 relative phase between HHG|| and HHG┴

Conditions are naturally met both in the vicinity of structural and dynamical minima

Circular dichroism “marks” dynamical minima in CO2

Circularity, calculated from recombination dipole for HOMO, no

angle averaging

Max circularity marks the positions of structural

minimumAfter averaging the min shifts from H25 to H37-39

HHG spectra, after averaging

HHG circularity

Max circularity marks the positions

of dynamical minima

I=2.0*1014W/cm2

Circular dichroism “marks” dynamical minima in CO2

H35: Harmonic phase for each channel

H35: HHG amplitudes for each

channel

H35: Circularity for each channel

Circularity indicates “switching” between different channels, and positions of

“dynamical” minima

I=2.0*1014W/cm2

Circularity of harmonics in CO2

– maximal number of harmonics with high circularity

I=2.0*1014W/cm2 I=1.5*1014W/cm2

High values of Mc shift to lower harmonic orders for lower intensity

Mc=(|Ez||Ex|sin(z-x))/ |Ex|2+ |Ez|2

Circularly polarized attosecond pulses

|ER|2- |EL|2

|ER|2+ |EL|2= |ER|- |EL|

|ER|+ |EL|=

150 asec pulse with Mc=0.7

I=2.0*1014W/cm2:

Conclusions

1. High circularity of harmonic light marks the positions of dynamical minima, background –free measurement

2. Structural minima can be hard to observe in polarization measurement

3. If the amplitude minimum is not accompanied by high circularity it is neither structural, no dynamical, but reflects switching from one dominant channel to another without destructive interference between them

4. Multichannel nature of HHG in molecules allow to shape polarization of asec pulses

Dynamical minimum in HH spectra

XB=(EX-EB) (N)+ rec+ion

1.1014

2.1014

3.1014

N= Ee()+Ip

N= 3.17 Up

Delay , fs

1.8 fs

Dynamical minimum shifts linearly with the intensity

Conclusions & Outlook

• HH spectroscopy

-identifies different molecular orbitals (electronic continua)

-records the interference between different electronic continua

-records attosecond dynamics of the hole left in the molecule via interference between different electronic continua (HH channels)

• HH spectroscopy: additional observables

-harmonic phases,

-harmonic polarizations circularity

Circular dichroism in HHG: Max circularity marks the positions of dynamical minima (background –free measurement)

I=2.0 1014 W/cm2

• HH spectroscopy can be used to study

-Multielctron dynamics in polyatomic molecules in strong fields

-Reconstruction of individual contributions of different orbitals vs intensity gives insight into the largely

unknown dynamics of strong field ionization in multielectron systems.

-Where is the hole created and how does it recoil from the departing electron? (done for CO2)

-How non-adiabatic laser induced transitions affect the dynamics of the hole? (current work - N2).

- Towards strong –field control of the hole shape and motion in polyatomic molecules (possibly leading to control of

fragmentation, charge transfer)

Non-linear optical wave-mixing (e.g.

HH-probe

Time-resolved PES

-Field-free coupled electronic and nuclear dynamics in polyatomic molecules via pump-HH probe schemes

-Field-free coupled electronic and nuclear dynamics in polyatomic molecules via UV pump-HH probe schemes

•Stimulated Raman Pumping of N-N stretch•HHG probing after t (800 nm strong field)

RAMANPUMP

HHGPROBE

Wen Li et al, Science 2008

IonIon*

PES HHS

HHS Observables: -amplitudes (spectra) -phases (!) -polarizations (!)Asec resolution

Selectivity: same initial and final state

HHS is inverse of PES +coherence in continuum

Harmonic phases near dynamical minimum

Structural minimum: -phase jumps

Dynamical minimum:

Ab-initio, 2D H2+, Lein et al, 2002

phase jumps near dynamical minima

I=2.0*1014W/cm2

I=1.3*1014W/cm2

Circular dichroism in HHG emission from aligned molecules

|ER|2- |EL|2

|ER|2+ |EL|2=

High circularity identifies switching between the channels

|ER|2- |EL|2

|ER|2+ |EL|2=

Mc indicates “switching” between different channels, and positions of “structural”

minima

|ER|2- |EL|2

|ER|2+ |EL|2=

Circular dichroism in HHG emission from aligned molecules

|ER|2- |EL|2

|ER|2+ |EL|2=

High circularity identifies switching between the channels

|ER|2- |EL|2

|ER|2+ |EL|2=

Mc indicates “switching” between different channels, and positions of “structural”

minima

|ER|2- |EL|2

|ER|2+ |EL|2=

Disentangling structural and dynamical information

Structural minimum:

Position of minimum is tied to the De-Broglie wavelength and hence energy of the continuum electron

(approximately intensity independent)

Dynamical minimum:

Position of minimum is tied to the time of recombination

(approximately linearly depends on intensity)

Modeling HHG: including different channels

j – labels different states of the ion

)(|d|)()(D )(Ie

)( ttt NNNEUT

jjCONT

NjIONb

N ttttt )()(A)]([a)( ,)1(

• NEUT (t) – MC SCF, quasi-static field, for all relevant electrons (CAS)

• ION, j (t)

• MC SCF for all (j=1..5) essential stationary ionic states, field-free

• Calculate all dipole couplings between these states

• Do TDSE dynamics in restricted basis of these ionic states

•Channel-specific Hartree potential : Hartree [ION,J]

• aion : syb-cycle YudinIvanov* orbital-dependent angular factor (CC-VGSFA)

• CONT , j (t) from SF EVA (Smirnova, Spanner, Ivanov PRA (2008))

)(|d|)()(D )(Ie

)( ttt NNNEUT

jjCONT

NjIONb

N ttttt )()(A)]([a)( ,)1(

Recombination matrix element: amplitude

k2/2+Ip=N

Harmonic order

Log scale

Harmonic order

Log scale

|dB|2 >> |dX|2

is not accidental – same nodal planes are at fault!

General whenever Dyson orbitals have nodal planes

|drec|2

Outlook

Each harmonic is a frame of an “attosecond movie” (M. Lein; S. Baker et al)

Longer wavelength - longer movie (~),

more frames per fs (~)

=1200nm

X,A channels~ ~

Contributions to XB~~

XB=(EB-EX) (N)+ rec~~ ~~

X≈B≈~ ~

if(EB-EX) << N

Recombination time, fs

X- B~~

N=Ee()+Ip

Destructive interference: XB=(2n+1) ~~

Harmonic number

XB=(EX-EB) (N)+ rec~~ ~~

Evolution of phase

Conclusions I -amplitudes

• Position of the HHG minimum is intensity dependent and is determined by the interplay of different channels

• Structural minimum is not easy to observe in HHG spectrum – the minimum is “filled” by the HH emission associated with other orbitals (other channels)

Conclusions II -phases

• Phase measurements can be very useful to

disentangle the contribution of different orbitals

• Phase jumps are often related to the switch

between the channels and do not have to be =

• Recombination matrix elements give the

dominant contribution into harmonic phases in

the case of CO2

phase jumps near interference minima

I=2.0*1014W/cm2

Molecular alignment angle, Molecular alignment angle,

Harmonic Phase, units of Harmonic Amplitude

I=1.3*1014W/cm2

Molecular alignment angle, Molecular alignment angle,

Harmonic Phase, units of Harmonic Amplitude

Role of electron-ion entanglement

Low degree of entanglement:

Eikonal vs exact, hydrogen atom

Eikonal vs plane wave

=20o =20o

=30o =30o

=40o =40o

Harmonic numberHarmonic number

|d|2 |d|2

Eikonal Plane wave

Contributions to XB

Harmonic number

DTOT= Dx(N)+ DB(N~~

Dx(N)=exp{-iV-iEXX(N)-irec,X}~

~DB(N)=exp{-iV-iEBB(N)-irec,B}

Destructive interference

XB=(2n+1) ~~

V<< XB if (N)<<(N~~

XB=(EX-EB) (N)+ rec~~ ~~

I=1014W/cm2

Angle of molecular alignment, deg

Switching orbitals: harmonic phases

Interpretation of NRC phase measurements

Yann Mairesse, Nirit Dudovich, Paul Corkum & David Villeneuve

Phase measurements @ NRC:

H21 H23

I=1014W/cm2Experiment vs TheoryH

H21 H23

I=1014W/cm2Experiment vs Theory

s of Harm

Conclusions I -amplitudes

• Position of the HHG minimum is intensity dependent and is determined by the interplay of different channels

• Structural minimum is not easy to observe in HHG spectrum – the minimum is “filled” by the HH emission associated with other orbitals (other channels)

Conclusions II -phases

• Phase measurements can be very useful to

disentangle the contribution of different orbitals

• Phase jumps are often related to the switch

between the channels and do not have to be =

• Recombination matrix elements give the

dominant contribution into harmonic phases in

the case of CO2

Main message

•HHG spectra for molecules reflect the contribution of different channels related to different states of the ion

•The relative contributions of these channels change with the intensity

•The positions of minima in HHG spectrum and phase jumps are often determined by the interplay of different channels

•The channels can be distinguished by looking at harmonics:

• amplitude,

• phase,

•photon energy

vs molecular orientation

(Example: CO2 molecule)

)(|d|)()(D )(Ie

)( ttt NNNEUT

jjCONT

NjIONb

N ttttt )()(A)]([a)( ,)1(

Visualization of hole dynamics X+A channels~ ~

X+B channels~ ~

Question: Where does the hole begin its motion?

Where does the hole start its motion?

ber cos4()

cos6()

The position of the minimum depends on the initial phase between the X and B channels: Xei+B

ber cos4()

cos6()

The position of the minimum depends on the initial phase between the X and B channels: Xei+B

•This dynamics can be further modified by the laser field (Not the case for CO2 in IR field)

•This dynamics is reflected in HHG spectra and we shall see how

High harmonic generation in molecules: a new spectroscopic toolLes entrées

•The basics of High Harmonic Generation• Attosecond measurements without attosecond pulses • Combining atto-second temporal and sub-A spatial resolution

Les plats

•Attosecond hole dynamics after tunnel ionization

Les desserts (add 7’)

Circular dichroism spectroscopy with high harmonics

Formule du Midi - 49’

ber cos4()

cos6()X&B channels~ ~

Direction of ionization

ber X+B channels

Direction of ionization

At low intensity the hole starts in the middle between the turning points: Xei/2+B

jCONTjIONN ttt )()(A)( ,,

BIONtiE

BXIONtiE

BCONTtiE

BIONXCONTtiE

•Wave-packet for CO2 molecules aligned along laser field

Recollision as a probe

V(x)+xELcost

X~EL/2 ~ 10-100 Å

Energy E~102 eV

DeBroglie< 1 Å

Electron probes the parent ion

•Elastic scattering

•Inelastic scattering

•Radiative recombination

)(|d|)()(D )(Ie

)( ttt NNNEUT

jjCONT

NjIONb

N ttttt )()(A)]([a)( ,)1(

Recollision after Tunnel Ionization

Corkum,1993, Schafer, Krause & Kulander, 1993

V(x)+xELcost

ionization

return

•This dynamics can be further modified by the laser field

(Not the case for CO2 in IR field)

•This dynamics is reflected in HHG spectra and we shall see how

HHG – multichannel interference

Neutral

Interference of light records relative phase between the channels

Let us look @ HHG spectra for different intensities

)()(D tDtj

)()(A|d|)()(D ,)1(

j tttt jCONTN

jIONNNEUT

Disentangling structural and dynamical information

Structural minimum:

Position of minimum is tied to the De-Broglie wavelength and hence energy of the continuum electron

(approximately intensity independent)

Dynamical minimum:

Position of minimum is tied to the time of recombination

(approximately linearly depends on intensity)

Theory vs experiment: HHG spectra

I~1*1014 W/cm2

I=1.26*1014 W/cm2

Alignment angle

onic order

Kinematics of Electron recollisionE

4 Recollision energy

3.17Up Up~10 eV

Scheme: Rev.Mod. Phys, Krausz, Ivanov

• In tunneling regime, the initial phase between and is zero, see frame 1: maximum extension in the direction of tunneling.

• Low intensity measurement (multiphoton regime) is consistent with frame 2: maximum delocalization

|X+B|2~~

|X-iB|2~ ~

|X-B|2~ ~

HH spectroscopy: Non-linear Optics perspective

Neutral

HH generation as a wave-mixing process

3Multiphoton regime

|X-B|2~~

|X-iB|2~ ~

|X+iB|2~ ~

Getting initial phase

BTotal

Destructive interference at

XB(*)=(2n+1)

Ee(+Ip=N

XB(=0)=?

Time scale

1 as = 1/1000 fs

Time10 sec100 as 10 billion years

We can apply strong laser fields to drive electrons and use them to image their own motion

• We can remove an electron from different orbitals

• Ion can be left in excited states

Many electrons and multiple orbitals

Ion Ion*

Different ionization channels-different HHG channelsDifferent ionization channels-different HHG channels

High harmonics: temporal resolution

Many different N are emitted at different times within 2 fsec

Atto-second temporal resolutionAtto-second temporal resolution

N2Ee(t)+Ip

0 2.6 t,fs

t - time delay between ionization and recombination

~e.g. 60 eV

2fs/20 odd harmonics~100 asec

Time and space resolved imaging of electron tunneling from molecules.

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