Attosecond light pulses for observing electron correlations in atoms

Toru MorishitaUniv. of Electro-

Communications Chofu, Tokyo

WithS. Watanabe (UEC)and C.D.Lin (KSU)

Improvements in ultra short pulse generation

Asec region

U. Keller, Nature 424, 831 (03) + private comm.

21st centuryAtto physics started in 21 century!

Attosecond in Atoms/Molecules

Rotation of molecules ： pico (10-12) sec

Vibration of molecules: femto (10-15) sec

Electron motion in atoms/molecules Classical period of electron in H atom

2π* 1 au = 150 asec

Real time analysis Control/manipulate

Atomic photographyNo ordinary camera can capture the motion of electrons inside an atom. But the advent of ultrafast laser pulses brings the necessary ‘shutter speed’ for snapping them as they tumble between energy levels close to the nucleus.

L F DiMauro, Nature 419, 789 (2002)

Electron motions in atoms

Structure of multi-electron atoms

Atom ， Wikipedia (Japanese)Uranium atom ， Max 　Ｗ　カーボン，原子力（それは加害者か被害者か）

Atom or molecule ? Completely different

(1s)2 (2s)2 ... Th , v, j, ...

Hartree-Fock(mean filed)

Born-Oppenheimer(adiabatic approximation)

)...ψ(r )ψ(rΨ 21 Ω)(R;Φ (R)FΨ μμ

Pauli’s exclusion principle ， Shell structure

Vibration around equilibrium position Overall rotation

Energy levels of Li+(3l3l’)E

nerg

y (e

V)

1Se 1De

1Se3Po

1Po

3Do

1Do

3Pe

1De

1De

3Fe

3Fo

1Fo1Ge

1Se

3Pe

3Po

3De

1Po

3s3s

3s3p

3s3d

3p3p

3p3d

3d3d

175

176

177

178

179

1Se

3Pe

3Po

1Po

3Do

1Do

1De

3De

1De

3Fe

3Fo

1Fo1Ge

1Se

3Pe

3Po

1Po

1De

1Se

175

176

177

178

179

“Atomic” picture “Molecular” picture

T 2 1 0 21 1 0 1 0

n=0

n=1n=2

E~EN+ ω(v+1)+B[L(L+1)-T2]+GT2

n=(v-T)/2

Hund’s rule

v=N-K-1

Correlated motions, 2s2 1Se and 2p2 1Se

Atomic orbital 〔 × 〕 Molecular picture ◎〔 〕

2s2 1Se

0 θ12 π

r1r2

θ12

2p2 1Se

(θ

12)

0 θ12π

0

0

“Ground state” w.r.t. θ12

“1st excited state” w.r.t. θ12

|K=−1 〉 = 0.88|2s2s 〉 +0.46|2p2p 〉|K=1 〉 = 0.46|2s2s − 〉 0.88|2p2p 〉

How can we see the correlated electron motion ?

2s2 1Se

0 θ12π

r1r2

θ12

2p2 1Se

(θ

12)

0 θ12π

0

Oscillation period

980 asec

0 θ12π

0

|(θ

12)|

2

Coherent Sum(Wave packet)

0

Visualization of electron correlations

Vibration |Φ(α, θ12)|2

ΩE=αEβEγE

(polar plots in body-fixed frame)

ψ≈F(R) Φ(α, θ12) D(ΩE)

vibration

Breathing Rotation r1

r2

α

R

θ12

r2r1

z

Hyperspherical coordinates

Rotation|D(ΩE)|2

2 e coincidence measurement

He**

pump probe

T=0 T=Tdela

y

p1

p2

Ionization prob dipole Ionization yield

Time evolution of the momentum space wave function

“Masking” function→１ (for T→0)

1. Gaussian2. 1st order purtarbation3. Direct product of the

plane waves (Final state)

4. Velocity gauge

Double ionization

2

~

ˆ

2kj

j 2

)Tε(

tiε21

jjj21

21

2

2121

e )e,(ct),,S(

t),,S( )(ε t),,P(

pppp

pppppp

Bending vibration

Period of the vibration:960 asec

θ12

p1//ε

p2

polarization

E1=E2=2.2eV

27.2 eV,200 asec

Vibrational motion, Tomographic imaging

p1

p2

αp

Rp

θp12

p2p1

Hyperspherical coordinates in momentume space

2s2 1Se + 2p2 1Se

Ep=27.2 eV, T=200 asecE1=E2=2.2eV

Rotational motion

z’

2s2 1Se + 2p2 1De

Molecular axis

Polar plots

z’

t=0 t=1fs t=2 fs

Double ionization yield, S

Detailed structure in momentum space

Ep=27.2 eV

Ep=54.4 eV

θp12

p2p1

θp12

p2p1

p1 =p2 p1 <p2

Low energy ：2electrons have the same energy

High energy ：1 has most of the energy

θp12

αp

2

2

)Tε(

tiε21

jjj21

2kj

j e )e,(~ct),,S(

pppp

T=200 asec

Rotation + Vibration

Vibration and rotation can be separated

Vibration(averaged over

rotational coordinates)

Rotation(averaged over

vibrational coordinates)

Pump-probe experiments

pump 　 (probability 10-3 - 10-4 )

He(1s2)

He **

(2s2, 2p2)

2 photons

2 color photons

1s2p

2s2p

Ti:Sa Laser + XUV

480 asec, 36.7 eV, 4x1014 W/cm2

480 asec, 38 eV,

4x1012 W/cm2

5 fsec, 1.5 eV,

4x1013 W/cm2

He ++

HHG from nsec laser

probe 　 (probability 10-3)

480 asec, 27.2 eV, 4x1012 W/cm2

•density ： 1 torr•Volume ： (10μm)2 x3mm350 events/shot

Summary

Probing molecule like motions of a 2 electron atom by asec pulses

Tomographic imaging of 2-e densities in momentum space

Coherent control

Many electron systemsT

Control/Manipulate wavepacket

Similar idea to coherent control of molecules

Frank-Condon Selective

excitation using 2 pulses

etc

Adia

batic

Pote

ntia

l

He(1Se)

Ground state

Hyperradius Ｒ

２ DOubly excited states

Uμ

selective excitations

Single pulse from 1s2p Double pulse from 1s2p

２ｓ

2s2 1Se

2p2 1Se

2p2 1De

Delay time

Ion

izati

on

pro

b

by p

um

p-p

rob

e

Ion

izati

on

pro

b.

by p

um

p

Electron energy Electron energy

Delay time

2p2 1Se

2s2 1Se

<θ

12>