Transcript Hyperspherical analysis of multiply excited states of atoms

Attosecond light pulses for
observing electron
correlations in atoms
Toru Morishita
Univ. of Electro-Communications
Chofu, Tokyo
With
S. Watanabe (UEC)
and C.D.Lin (KSU)
Improvements in ultra short pulse generation
Atto physics started in 21 century!
21st century
Asec region
U. Keller, Nature 424, 831 (03) + private comm.
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 photography
No 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
Hartree-Fock
(mean filed)
Pauli’s exclusion principle，
Shell structure
(1s)2 (2s)2 ...
Ψ  ψ(r1 ) ψ(r2 )...
Born-Oppenheimer
(adiabatic approximation)
Vibration around equilibrium position
Overall rotation
Th , v, j, ...
Ψ  Fμ (R) Φμ (R;Ω)
Energy levels of Li+(3l3l’)
“Molecular” picture
“Atomic” picture
Hund’s rule
E~EN+ ω(v+1)+B[L(L+1)-T2]+GT2
1Se
Energy (eV)
n=1
179
179
n=0
1Po
3Pe
178
178
1Po
1De
177
1De
1 Se
3De
176
175
1 Po
1Se
3Po
3Po
3Do
1Do
3 Pe
1Ge
1Ge 1Fo
177
3Fe
176
3Fo
3Fe
175
3Po
3Do
1De
1Do 3Fo
3Pe
1De
1De
3De
1Se
1Po
3Po
1Se
3s3s 3s3
p
3s3d 3p3p 3p3
d
3d3d
n=2
3P e
1De
1Fo
1Se
T
2 1 0 1 2
n=(v-T)/2
v=N-K-1
1 0 1
0
Correlated motions, 2s2 1Se and 2p2 1Se
Atomic orbital〔×〕 Molecular picture〔◎〕
2s2 1Se
2p2 1Se
|K=−1〉=0.88|2s2s〉+0.46|2p2p〉
“1st excited state” w.r.t. θ12
(θ12)
“Ground state” w.r.t. θ12
0
|K=1〉=0.46|2s2s〉 − 0.88|2p2p〉
0
θ12
0
r2
θ12
r1
π
0
θ12
π
How can we see the correlated electron motion ?
θ12
2s2 1Se
r1
(θ12)
r2
2p2 1Se
0
0
0
0
π
θ12
θ12
π
|(θ12)|2
Coherent Sum
(Wave packet)
0
Oscillation period
980 asec
0
θ12
π
Visualization of electron correlations
Hyperspherical coordinates
ψ≈F(R) Φ(α, θ12) D(ΩE)
Breathing vibration Rotation
Vibration
|Φ(α, θ12)|2
Rotation
|D(ΩE)|2
ΩE=αEβEγE
(polar plots in body-fixed frame)
r1
r2
r2
θ12
z
R
α
r1
2 e coincidence measurement
T=Tdelay
T=0
Double ionization
p2
He**
pump
probe
Ionization prob
Ionization yield
dipole
P(p1 , p 2 , t)  εˆ  (p1  p 2 )
S(p1 , p 2 , t) 
p1
2
1.
2.
3.
S(p1 , p 2 , t)
~ (p , p )e iε jt e
c

 j j 1 2
 (  ε kj )T 


2


2
2
4.
j
Time evolution of
“Masking” function
the momentum
space wave function →１(for T→0)
Gaussian
1st order purtarbation
Direct product of the
plane waves (Final state)
Velocity gauge
Bending vibration
Period of the vibration:
960 asec
27.2 eV,200 asec
p2
E1=E2=2.2eV
θ12
p1//ε
polarization
Vibrational motion, Tomographic imaging
2s2 1Se + 2p2 1Se
Hyperspherical coordinates in
momentume space
p2
Rp
αp
p1
p1
p2
θp12
Ep=27.2 eV, T=200 asec
E1=E2=2.2eV
Rotational motion
2s2 1Se + 2p2 1De
Molecular axis
t=0
t=1fs
Polar plots
Double ionization yield, S
z’
t=2 fs
z’
Detailed structure in
momentum space
S( p1 , p 2 , t) 
 c ~ (p , p )e
iε j t
j
j
1
2
j
T=200 asec
Ep=27.2 eV
Ep=54.4 eV
αp
θp12
Low energy：
2electrons have the same energy
p1 =p2
p1
p2
θp12
High energy：
1 has most of the energy
p1 <p2
p1
p2
θp12
e
 ( ε kj )T 


2


2
2
Rotation + Vibration
Vibration
(averaged over
rotational coordinates)
Rotation
(averaged over
vibrational coordinates)
Vibration and rotation can be separated
Pump-probe experiments
pump (probability 10-3 - 10-4 )

2 photons
480 asec, 36.7 eV,
4x1014 W/cm2
He
2 color photons
Ti:Sa Laser + XUV
480 asec, 38 eV,
5 fsec, 1.5 eV,
4x1012 W/cm2
4x1013 W/cm2
++
2s2p
He **
(2s2, 2p2)
1s2p
He(1s2)
HHG from
nsec laser
probe (probability 10-3)

480 asec, 27.2 eV, 4x1012 W/cm2
•density：1 torr
•Volume： (10μm)2 x3mm
350 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
T

Many electron systems
Control/Manipulate wavepacket




Frank-Condon
Selective
excitation using
2 pulses
etc
Adiabatic Potential
Similar idea to
coherent control
of molecules
２DOubly excited states
Ground state
Uμ
He(1Se)
Hyperradius Ｒ
selective excitations
Ionization prob.
by pump
Single pulse from 1s2p
2p2 1De
2p2 1Se
２
ｓ
2s2 1Se
Double pulse from 1s2p
2s2 1Se
2p2 1Se
Electron energy
<θ12>
Ionization prob
by pump-probe
Electron energy
Delay time
Delay time