Attosecond applications in atoms - ATTOFEL — .:ATTOFEL:. · Quantum state holography ... Study of electronic correlation Helium: TPDI Sequential TPDI Non Sequential TPDI. TPDI:

Attosecond applications in atomsAttosecond applications in atoms

G. Sansone

ATTOFEL Summer School

Crete 06/05/2011

OutlineOutline

1) Hydrogen

single electron

coherent bound wave packetscoherent bound wave packets

2) Helium

two-electrons electron correlation

coherent bound wave packets, autoionization, double ionizationcoherent bound wave packets, autoionization, double ionization

3) Multi-electrons (n>2) atoms (noble gases: Neon, Argon, Krypton, Xenon)

valence and core electrons

auger decay; shake up statesauger decay; shake up states

Outline

Dynamics and wave packetsDynamics and wave packets

• Ground state (or eigenstate of hamiltonian H)

No dynamics

• Electronic wave packet:

Timescale of dynamics:

)()()/exp()()(),( 3 rprr pp ψψψ tbdtiEtat jjj

j ∫∑ +−= h

)/exp()(),( htiEt jj −= rr ψψ

li EE

hT

−=

Introduction

Hydrogen: Hydrogen: coherent superposition of statescoherent superposition of states

)/exp()()/exp()(),( 222111 hh tiEatiEat ssssss −+−= rrr ψψψ

eV4.38

1

)2/exp()2/1(22

1)(

eV5.132

1

)/exp(1

)(

2

002/30

2

1

02/30

1

−=−=

−−=

−=−=

−=

aus

s

aus

s

EE

arara

EE

ara

πψ

πψ

r

r

1s state

2s state

Hydrogen Coheren wave packet

0a Bohr radius auE Atomic unit of energy

eV1.1012 =−=∆ ss EEE

Hydrogen: Hydrogen: space/momentum representationspace/momentum representation

)/exp()()/exp()(),(

)/exp()()/exp()(),(

222111

222111

hh

hh

tiEatiEat

tiEatiEat

ssssss

ssssss

−+−=

−+−=

ppp

rrr

φφφ

ψψψ

2

121 == ss aa

00 / ap h=Hydrogen Coherent wave packet

Coherent superposition of 1sCoherent superposition of 1s --2s: 2s: attosecond attosecond ““ breathingbreathing ”” motionmotion

Space

(unit of a0)

Momentum

(unit of p0)

Hydrogen Coherent wave packet

as400=T

Excitation and imaging of attosecond motionExcitation and imaging of attosecond motion

A. Scrinzi, M. Geissler, T. Brabec, Laser Phys 11, 169 (Feb, 2001).


1) Coherent excitation (well defined phase) requires attosecond pulsesPump: attosecond pulse (1s->2p transition)+intense static field

(1s-> 2s transition is dipole forbidden)

2) Imaging of the breathing motion requires attosecond pulsesProbe: attosecond pulse to photoionize the atom

Excitation and imaging of attosecond motionExcitation and imaging of attosecond motion

A. Scrinzi, M. Geissler, T. Brabec, Laser Phys 11, 169 (Feb, 2001).


1) Coherent excitation (well defined phase) requires attosecond pulsesPump: attosecond pulse (1s->2p transition)+intense static field

(1s-> 2s transition is dipole forbidden)

2) Imaging of the breathing motion requires attosecond pulsesProbe: attosecond pulse to photoionize the atom

ionization yield depends on the delay

tEE ss

h

12 −=∆Φ

Two interfering terms due to ionization from the

1s and 2s states:

HeliumHelium

A. Imaging of coherent bound wave packet

B. Autoionization-> Fano resonance

C. Two photon double ionization

+

+

=

∫ ∫

∑∫

∑

),()('

),()(

),()(

),,(

21''33

21,3

21,

21

rrpp

rrp

rr

rr

pppp

pp

ψ

ψ

ψ

ψ

tbdd

tbd

tc

ti

i

ijji

ij Bound states

Single ionization

Double ionization

Helium

A. B.

C.

EElectronlectron icic wave packetwave packet //HHolographyolography

Object beam

Reference beam

oψ

rψ

*22Re2 ororS ψψψψ ++=

Helium

LaserBeam

splitter Object

)]/(exp[)( nnnn

no tEita ϕψψ +−=∑ h

QQuantumuantum state holographystate holography“Object”

“Reference”

“Unknown”

“Known”

“Signal”

C. Leichtle et al. Phys. Rev. Lett. 80, 1418 (1998)

1. Attosecond XUV pump- IR probe approach

2. Observable: angular resolved photo-electron spectra (for different delays)

nn

nr dti ψφψ ∑= )](exp[

))]((exp[Re2 *22ttEidadaS nnnnnnn φϕ ++−++=

Complete characterization method :

• Amplitudes an(t), energies E

nand initial phases ϕ

n

Helium

Experimental setup: single attosecond pulse Experimental setup: single attosecond pulse

20 24 28 32 360.0

0.2

0.4

0.6

0.8

1.0

Inte

nsity

(ar

b. u

nits

)

Photon energy (eV)

Spectrum generated in Xenon

eV4.241 =sE

XUV continuum generated by the

Polarization Gating method

Al filter

λ/4plates

Xe cell

SiO2

plate

Translation stage

Toroidal mirror

RepellerHe jet

ExtractorMCP+CCD

VMIS

Helium

Velocity Map Imaging of Electron Dynamics• very high collection efficiency (up to 100%)• energy AND angular information

3D distribution 2D image

Slice throughreconstructed distribution

Experimental setup: Experimental setup: Velocity Map Imaging SpectrometerVelocity Map Imaging Spectrometer

px

py θ0°

90°

180°

270°

A.T.J.B. Eppink and D.H. Parker, Rev. Sci. Instrum. 68, 3477 (1997)

XUV pulse

IR pulse

Obtain 3d-momentum distributions !

energy & angular information

Extraction

Detection

Electrons

Repeller

Helium

Object (superposition of states)+Object (superposition of states)+ refencerefence

Broadband attosecond pulse : Broadband attosecond pulse : Creation of a bound wave packet (object)Creation of a bound wave packet (object)

and a free wave packet (reference)and a free wave packet (reference)

Helium

2p

3p

4p

continuum

Object (superposition of states)+Object (superposition of states)+ refencerefence

Signal

mpnp EE −hπ2

EEnp −hπ2

Broadband attosecond pulse : Broadband attosecond pulse : Creation of a bound wave packet (object)Creation of a bound wave packet (object)

and a free wave packet (reference)and a free wave packet (reference)

IR field projection of the bound wave packet in the continuum:IR field projection of the bound wave packet in the continuum:Interference fringes between the two paths!Interference fringes between the two paths!

Helium

Bound-continuum Bound-bound

Theoretical results in Helium Theoretical results in Helium EExcitation with a SAP around the threshold xcitation with a SAP around the threshold -- probe with an IR pulseprobe with an IR pulse

XUV-IR delay (IR cycles)

1 2 3 4 5

En

erg

y (

eV

)

15

10

5

-5

-10

-15

Energy and delay dependent fringes

Bound-continuum components

Beating @ 2 eV

Bound-bound components

Typical “streaking” pattern:

XUV and IR fields overlapped

6 7 8 9 10 11 12 13

IR after SAP

Helium

Delay (optical cycle)

Fourier analysisFourier analysis

-15 -10 -5 0 5 10 15

15

10

5

Energy (eV)

Energy independent2p-3p beating

2p-continuum oscillation

3p-continuum oscillation

Energy dependentBound-continuum beating

Intersection with Zero: Bound State Energies

En

erg

y (

eV

)

Helium

Experimental results: short delay scanExperimental results: short delay scan

Up

Down

Time

Energy

Helium

J. Mauritsson et al., Phys Rev Lett 105, (Jul 27, 2010).

Experimental results: long delay scanExperimental results: long delay scan

QB

Helium

J. Mauritsson et al., Phys Rev Lett 105, (Jul 27, 2010).

Autoionization processAutoionization process

E1s

E=0

Direct ionization

1s2

eV60≅ωh

ωh

eVEk 6.35≅

Helium: autoionization


E1s

E=0 E=0

Direct ionization Doubly excited

states

1s2 1s2

2s2p

eV60≅ωh

ωh ωh

eVEk 6.35≅



E1s

E=0 E=0 E=0

Direct ionization Doubly excited

states

1s2 1s2 1s2

2s2p

T

eV60≅ωh

ωh ωh

eVEk 6.35≅ eVEk 6.35≅

Autoionization


Autoionization: Fano profileAutoionization: Fano profile

2

EVπ=Γ

Γ= /1T

∫+=Ψ '' )(')( EE tbdEta ψϕ

ϕψ HV EE =Coupling between the bound state

and the continuum states

Autoionization time

Fano profileDoubly excited

states

Continuum states:

The first electron is bound

The second electron is free


U. Fano, Phys. Rev. 124, 1866 (1961).

Linewidth

Time resolved autoionizationTime resolved autoionization

S. Gilbertson et al., Phys Rev Lett 105, (Dec 27, 2010).


ττττ=delay

Time resolved autoionizationTime resolved autoionization


AI=autoionization signal at 34.5 eV

SB1=sideband generated by the autoionizing electron+IR

SB2=sideband generated by the autoionizing electron-IR


ττττ=delay

1s2

Direct Auto

Autoionization timeAutoionization time



• T=17 fs

Two photon double ionization of HeliumTwo photon double ionization of Helium(TPDI)(TPDI)

1.1. Nonlinear process in the XUV regionNonlinear process in the XUV region

2.2. Characterization of the duration of XUV pulses Characterization of the duration of XUV pulses (autocorrelation techniques)(autocorrelation techniques)

3.3. FEL or high energy driving pulses for HHGFEL or high energy driving pulses for HHG

4.4. Study of electronic correlationStudy of electronic correlation

Helium: TPDI

Two photon double ionization of HeliumTwo photon double ionization of Helium(TPDI)(TPDI)

1.1. Nonlinear process in the XUV regionNonlinear process in the XUV region

2.2. Characterization of the duration of XUV pulses Characterization of the duration of XUV pulses (autocorrelation techniques)(autocorrelation techniques)

3.3. FEL or high energy driving pulses for HHGFEL or high energy driving pulses for HHG

4.4. Study of electronic correlationStudy of electronic correlation

Helium: TPDI

Sequential TPDI Non Sequential TPDI

TPDI: Sequential double ionizationTPDI: Sequential double ionization

22

11

p

s

IE

EE

−=−=

ωωh

h

Sequential absorption

ωh

Helium: TPDI

ωh

1E

2E

He+He

TPDI: Sequential double ionizationTPDI: Sequential double ionization

22

11

p

s

IE

EE

−=−=

ωωh

h

EIE

EEE

p

s

∆+−=∆−−=

22

11

ωωh

h

Sequential absorption Sequential absorption

with shake-up

(electron correlation)

ωh

Helium: TPDI

ωh

1E

2E

He+He

TPDI: NonTPDI: Non --sequential double ionizationsequential double ionization

E1s

ωh ωh

2/)( 2121 ps IEEE +−== ωh

Helium: TPDI

TPDI: NonTPDI: Non --sequential double ionizationsequential double ionization

The two photons are adbsorbed “simultaneously”

2121 2 ps IEEE −−=+ ωh

E1sE1s

ωh ωh

(electron correlation)2/)( 2121 ps IEEE +−== ωh

Helium: TPDI

Sequential vs NonSequential vs Non --sequentialsequential

The difference between sequential and non-sequential processes

is valid only in the long pulse limit

Timescale of the core relaxation process:

He2+

He2+ He

2+

He

(E1s=24.6 eV)He++e He+

(Ip2=54.4 eV)

as22)/( 12 =−=∆ sp EIt h

Helium: TPDI

Two photon double ionizationTwo photon double ionization

K. L. Ishikawa, K. Midorikawa, Phys Rev A 72, (Jul, 2005).

eV4.91=ωh as450=τ

Helium: TPDI

Two photon double ionizationTwo photon double ionization


eVIEEE ps 8.1032 2121 =−−=+ ωheV4.91=ωh as450=τ

Helium: TPDI

Sequential double ionizationSequential double ionization


eVIE

eVEE

p

s

37

8.66

22

11

=−==−=

ωωh

h

eHesHe

esHeHe

+→+

+→+++

+

2)1(

)1(

ωω

h

h

Helium: TPDI

Sequential double ionization:Sequential double ionization:shakeshake --up statesup states


eVEIE

eVEEE

p

s

8.77

26

22

11

=∆+−==∆−−=

ωωh

h

eVE 8.40=∆

eHepsHe

epsHeHe

+→+

+→+++

+

2)2,2(

)2,2(

ωω

h

h

Helium: TPDI

NonNon --Sequential double ionization:Sequential double ionization:anomalous componentanomalous component


Helium: TPDI

Anomalous component: pulse durationAnomalous component: pulse durationas150=τas225=τ

Broadening due to the bandwidth

of the attosecond pulse

Helium: TPDI

Anomalous component: pulse durationAnomalous component: pulse durationas150=τas225=τ

Broadening due to the bandwidth

of the attosecond pulse

red line : integration over E2

blue line : fit with two gaussians

black dotted line: fit with the two-photon

absorption profile

The anomalous component

requires a description

of electron correlation

Helium: TPDI

Helium : configuration interactionHelium : configuration interaction

...,

),(

,

),(

,

),( +++= ∑∑∑ jdidji

jidjpip

ji

jipjsis

ji

jis aaa ψψψψψψψ

)()(),( 211121 rrrr ss ψψψ ≅ Hartree-Fock (indipendent particle)

is represented by the combination of different configurations

)](cos)(cos1[4 42

0 θγθβπ

σσPP

d

d ++=Ω

Electron correlation are encoded in the

photo-electron angular distribution

42,PPLegendre Polynomials

dipole emission -> indipendent particle

quadrupolar emission -> correlated particles

Helium: TPDI

ψ

γβ

Angular distribution: dipole emissionAngular distribution: dipole emission

17.0

87.1

391

−===

γβ

eVE),( f

xuvif

xuvi psps →→

Helium: TPDI

I. F. Barna, J. Y. Wang, J. Burgdorfer, Phys Rev A 73, (Feb, 2006).

35.0

51.0

521

===

γβ

eVE

Angular distribution: quadrupole emissionAngular distribution: quadrupole emission

Helium: TPDI

),( fxuvxuv

ifi dpsss →→→),( f

xuvif

xuvi dpsp →→I. F. Barna, J. Y. Wang, J. Burgdorfer, Phys Rev A 73, (Feb, 2006).

MultiMulti --electrons systemselectrons systems

• Valence electrons

• Inner-valence electrons (tens of eV)

• Core electrons ( keV)

• Relevance of electronic correlation:

i. Fano resonances

ii. Shake-up states

iii.Auger decay

iv.Cascaded Auger decay

Multi-electron systems

MultiMulti --electrons systemselectrons systems

Multi-electron systems

NEON

1s22s22p6

ARGON

1s22s22p6 3s23p6

KRYPTON

1s22s22p6 3s23p6

3d104s24p6

XENON

1s22s22p6 3s23p6

3d104s24p6 4d105s25p6

Shake-up states

Tunnelling

spectroscopy

Fano resonance

Transient absorption

spectroscopy

Auger decay

Attosecond streaking

Cascaded Auger

Decay

Ion chronoscopy

Cascaded Auger

decay

Intense XUV pulses

(LCLS)

Hole oscillation

Transient absorption

spectroscopy

Autoionization

XUV pump-XUV probe

Multi-electron systems: Krypton

Krypton: auger decayKrypton: auger decay

3d

4s

4p

Kr+

1) Ionization of an electron of the 3d shell


Krypton: auger decayKrypton: auger decay

3d

4s

4p

Kr+ Kr2+

τ

1) Ionization of an electron of the 3d shell

2) An electron of the 4s shell fills the hole

3) The excess energy is transferred to a 4p electron that is emitted

Auger decay: sidebandsAuger decay: sidebands


Kr2+

τ= 7 fs

1) Depletion of the Auger peak

2) Sidebands : time overlap between the

Auger lifetime and the IR pulse duration

M. Drescher et al., Nature 419, 803 (Oct 24, 2002).

-21.5 eV

1s

2s

2p

Multi-electron systems: Neon

Neon: energy levels and excitation energyNeon: energy levels and excitation energy

E

-48.5 eV

-870 eV

0 eV

E 90 eV 800 eV

1050 eV

2000 eV

90 eV 50-60 eV

Levels 2p 2p-2s

1s-2s-2p

1s-2s-2p

2s and 2p 2s

Process Excitation of

shake-up

states

Cascaded Auger

Decay

Delay in

photoemission

Interatomic

Coulombic Decay

(neon dimers)

-21.5 eV

1s

2s

2p


Neon: energy levels and excitation energyNeon: energy levels and excitation energy

E

-48.5 eV

-870 eV

0 eV

E 90 eV 800 eV

1050 eV

2000 eV

90 eV 50-60 eV

Levels 2p 2p-2s

1s-2s-2p

1s-2s-2p

2s and 2p 2s

Process Excitation of

shake-up

states

Cascaded Auger

Decay

Delay in

photoemission

Interatomic

Coulombic Decay

(neon dimers)

1) Ionization from the 2p level by 90 eV

2) Excitation of a second 2p electron to an

excited ionic states

1s

2s

2p

2p-2nl


Neon: shakeNeon: shake --up statesup states

1) Ionization from the 2p level by 90 eV

2) Excitation of a second 2p electron to an


3) Ionization of excited state by an IR field

4) Doubly charged ions

1s

2s

2p

2p-2nl



1) Ionization from the 2p level

2) Excitation of a second 2p level to an


3) Ionization of excited state by an IR field

4) Doubly charged ions

1s

2s

2p

2p-2nl



Neon: tunnelling ionizationNeon: tunnelling ionization

M. Uiberacker et al., Nature 446, 627 (Apr 5, 2007).

















Ion chronoscopy: Auger time scale in XenonIon chronoscopy: Auger time scale in Xenon



1) 4d ionization of Xenon by 90-eV radiation

2) Relaxation by single (A1) and cascaded (A1 and A2) Auger decays

3) Formation of Xe2+ and Xe3+

4) Formation of Xe 4+ by the IR

Xe

Xe+

Xe2+

A1

Xe3+ Xe3+

A2

Xe4+

Ion chronoscopy: Auger time scale in XenonIon chronoscopy: Auger time scale in Xenon



1) 4d ionization of Xenon by 90-eV radiation

2) Relaxation by single (A1) and cascaded (A1 and A2) Auger decays

3) Formation of Xe2+ and Xe3+

4) Formation of Xe 4+ by the IR

Xe

Xe+

Xe2+

A1

Xe3+ Xe3+

A2

Xe4+

A) Decay times of the Auger processes

B) Follow in time the population of the different levels


Neon: highly charged ions by keV radiationNeon: highly charged ions by keV radiation

L. Young et al., Nature 466, 56 (Jul 1, 2010).

-21.5 eV

1s

2s

2p

E

-48.5 eV

-870 eV

0 eV

Experiment at LCLS

Energy Epulse=2.4 mJ


Neon: highly charged ionsNeon: highly charged ions


-21.5 eV

1s

2s

2p

E

-48.5 eV

-870 eV

0 eV

Experiment at LCLS

Energy Epulse=2.4 mJ


Neon: ionization dynamics at 2000 eVNeon: ionization dynamics at 2000 eV


1s

2s

2p

Ne+




1s

2s

2p

Ne+ Ne2+




1s

2s

2p

Ne+ Ne2+ Ne3+


Neon: XNeon: X --ray induced transparencyray induced transparency


1s

2s

2p

Ne+ Ne2+ Ne3+

Photo-absorption decreases with

shorter pulse duration Intensity induced X-ray transparency


Neon: double core hole at 2000 eVNeon: double core hole at 2000 eV


1s

2s

2p

Ne+ Ne2+

Electron spectra

Formation of hollow atoms

Argon: Fano resonanceArgon: Fano resonance

H. Wang et al., Phys Rev Lett 105, (Oct 1, 2010).

Multi-electron systems: Argon

3s2

3p6




3s

3p6

3s3p66p

3s3p65p

3s3p64p

Autoionizing

states

eV28≅ωh




3s

3p6

3s3p66p

3s3p65p

3s3p64p

Autoionizing

states

XUV absorption spectrum

eV28≅ωh

Fano resonance: Fano resonance: transient absorption spectroscopytransient absorption spectroscopy


I=5x1012 W/cm2I=5x1011 W/cm2


Fano resonance: Fano resonance: transient absorption spectroscopytransient absorption spectroscopy


I=5x1011 W/cm2 I=5x1012 W/cm2

1) Broadening of the lines –> shorter lifetime

2) Shift of the central energy

3) Splitting of the resonance at high intensity (3s3p64p)

IR induced couplings in Fano resonanceIR induced couplings in Fano resonance


Coupling between the 5p and 6p to the Ar*+

reduction of the lifetime-broadening of the line

IR induced couplings in Fano resonanceIR induced couplings in Fano resonance


Coupling between the 4p and 4d resonance

Splitting of the peaks

Krypton: strong field ionizationKrypton: strong field ionization

E. Goulielmakis et al., Nature 466, 739 (Aug 5, 2010).


Generation of a coherent superposition of two ionic states by IR

ionization

p41

2/1

−

p41

2/3

−

4p-1

Kr+

6.2fsTeV67.0 =→=∆E

Spin-orbit splitting

Imaging of hole oscillation:Imaging of hole oscillation:transient absorption spectroscopytransient absorption spectroscopy


tE

h

∆=∆Φ

Modulation of tha absorption of the XUV :

two interfering paths

dp

dp

3434

1

2/3

1

2/3

1

2/3

1

2/1

−−

−−

→

→

E. Goulielmakis et al., Nature 466, 739 (Aug 5, 2010).

ConclusionsConclusions

Conclusions

• Hydrogen

Imaging of coherent superposition of 1sImaging of coherent superposition of 1s--2s states2s states

• Helium

Relevance of electron correlation in Fano resonance Relevance of electron correlation in Fano resonance and TPDIand TPDI

• Multi-electrons atoms

Single and cascaded Auger decaysSingle and cascaded Auger decays

ShakeShake--up statesup states

Complex Fano resonancesComplex Fano resonances

Documents

Attosecond applications in atoms - ATTOFEL — .:ATTOFEL:. · Quantum state holography ... Study of electronic correlation Helium: TPDI Sequential TPDI Non Sequential TPDI. TPDI: