Transcript Document

Fragmentation Dynamics of H2+ / D2+
in Intense Ultrashort Laser Pulses
U. Thumm
Kansas State University
B. Feuerstein
T. Niederhausen
• Introduction
• Method of Calculation
• Results: initial vibrational state dependence
intensity dependence
pump-probe study of coherent vibrational motion
INTRODUCTION
Laser pulse (Ti:sapphire)
H2+ (D2+)
Time scales
Tcycle = 2.7 fs
Telectr = 0.01 fs
Tpulse = 5 -150 fs
Tv=0 = 14 (20) fs
Energies
Ip = 30 eV
 = 1.5 eV
( ˆ 20 )
De = 2.8 eV ( ˆ 2 )
Length scales
l = 16000 a.u. (800 nm)
R0 = 2 a.u.
H0 + H+ dissociation
2
1
H2+
H2
4
3
H+ + H+ Coulomb explosion
1
single ionization
2
dissociation
3
enhanced ionization (CREI)
4
fast Coulomb explosion
Dissociation and Ionization paths
weak field
1.0
0
p+p
0.8
1
CE
2
0.6
strong field
0
E [a.u.]
3
0.4
Charge resonance
enhanced ionization
0.2
H2+
u
1
0.0
1
g
2
2(3)
3
Dressed potential curves
(schematic)
-0.2
0
5
10
R [a.u.]
15
METHOD OF CALCULATION
Laser field
z
p
2x1D model
p
eR
Hˆ  TˆR  1/ R  Tˆz  Vsce  Vlaser
Vlaser  E(t ) cos(t )  z
2D Crank-Nicholson split-operator propagation
( z, R, t  t )  e
 i TˆR t / 2
 O( t 3 )
e
 i (Tˆz 1/ R Vsce Vlaser ) t
e
 i TˆR t / 2
( z, R, t )
Improved soft-core Coulomb potential
Fixed softening parameter a = 1
~) 
Vsce ( z
1
~2  a
z
~  z R/2
z
(Kulander et al PRA 53 (1996) 2562)
R-dep. softening function a(R)
+ fixed shape parameter b = 5
Vsce( ~
z)
1
~
z 2  ( a( R ) b )2  1 a( R )  a( R ) b
present result
a(R) adjusted to
(exact) 3D pot. curve
Dipole oscillator strength for sg – su transitions
Dipole(R)   su ( z; R ) z sg ( z; R ) dz
5
Dipole [a.u.]
4
3
2
} Kulander et al
PRA 53 (1996) 2562
1
This work (1D)
0
0
2
4
6
R [a.u.]
8
10
Array for 2x1D collinear non-BO wave packet propagation
“virtual detector” method
z: electron coordinate
R: internuclear distance
Grid: z = 0.2 a.u.; R = 0.05 a.u.
“virtual detector”: data analysis
(z, R, t )  A( z, R, t ) ei  ( z,R,t )
j R ( z, R, t ) 
 
 ( z, R, t )    v R ,
 R
  A( z, R, t )
Dissociation
(D )
pR
( z, t ) 

 ( z, Rdet , t )
R
Integration over z and binning  fragment momentum distribution
Coulomb explosion

pR ( zdet , t ) 
 ( zdet , R, t )
R
(CE )
pR
(R, t ) 
2
pR
( zdet , R, t )  2 R
Integration over R and binning  fragment momentum distribution
2
RESULTS
Time evolution of wave function and norm (on numerical grid)
Evolution of nuclear probability density (R,t )
dissociation probability
ionization rate jz(R,t)
CE probability
Kinetic energy spectra of the fragments
A) Single pulse (I = 0.05 – 0.5 PW/cm2, 25 fs):
vibrational state and intensity dependence
B) Pump-probe pulses (I = 0.3 PW/cm2, 25 fs):
CE-imaging of dissociating wave packets
C) Ultrashort pump-probe pulses (I = 1 PW/cm2, 5 fs):
CE-imaging of bound and dissociating wave packets
v=4
0.2 PW/cm2
25 fs
PCE(t)
Dissociation
PD (t)
Norm(t)
Laser
Coulomb explosion
a
- - - - - (Coulomb energy)
30
a b c
25
c
d
d
b
20
total fragment energy [eV]
15
(R,t ) 
zdet

2(3) 
2
( z, R, t ) dz
 zdet
10
V
0
19
log scale
Contours: jz(R,t)
5
1
V 5
0
0
0
20
40
60
80
100
120
140
160
180
200
19
2
4
6
8
10
Norm(t)
v=0
0.2 PW/cm2
25 fs
Dissociation
Coulomb explosion
Laser
PD (t) PCE(t)
(R,t ) 
zdet

- - - - - (Coulomb energy)
2(3) 
2
( z, R, t ) dz
 zdet
V
0
19
log scale
1
V 5
0
19
2
4
6
8
10
v=2
0.2 PW/cm2
25 fs
PCE(t)
PD (t)
Norm(t)
Dissociation
Coulomb explosion
Laser
- - - - - (Coulomb energy)
30
25
20
15
(R,t ) 
zdet

2(3) 
2
( z, R, t ) dz
 zdet
10
V
0
19
log scale
Contours: jz(R,t)
5
1
V 5
0
0
0
20
40
60
80
100
120
140
160
180
200
19
2
4
6
8
10
v=4
0.2 PW/cm2
25 fs
PCE(t)
Dissociation
PD (t)
Norm(t)
Laser
Coulomb explosion
a
- - - - - (Coulomb energy)
30
a b c
25
c
d
d
b
20
15
(R,t ) 
zdet

2(3) 
2
( z, R, t ) dz
 zdet
10
V
0
19
log scale
Contours: jz(R,t)
5
1
V 5
0
0
0
20
40
60
80
100
120
140
160
180
200
19
2
4
6
8
10
PCE(t)
v=6
0.2 PW/cm2
25 fs
Dissociation
PD (t)
Norm(t)
Laser
Coulomb explosion
- - - - - (Coulomb energy)
30
25
20
15
(R,t ) 
zdet

2(3) 
2
( z, R, t ) dz
 zdet
10
V
0
19
log scale
Contours: jz(R,t)
5
1
V 5
0
0
0
20
40
60
80
100
120
140
160
180
200
19
2
4
6
8
10
PCE(t)
v=8
0.2 PW/cm2
25 fs
Dissociation
Laser
PD (t)
Norm(t)
Coulomb explosion
- - - - - (Coulomb energy)
30
25
20
15
(R,t ) 
zdet

2(3) 
2
( z, R, t ) dz
 zdet
10
V
0
19
log scale
Contours: jz(R,t)
5
1
V 5
0
0
0
20
40
60
80
100
120
140
160
180
200
19
2
4
6
8
10
Branching ratio : Dissociation vs. Coulomb explosion
RESULTS II
A) Single pulse (I = 0.05 – 0.5 PW/cm2, 25 fs):
vibrational state and intensity dependence
B) Pump-probe pulses (I = 0.3 PW/cm2, 25 fs):
CE-imaging of dissociating wave packets
C) Ultrashort pump-probe pulses (I = 1 PW/cm2, 5 fs):
CE-imaging of bound and dissociating wave packets
Pump-probe experiment
2(3) 
1
CE
D2 target
0.1 PW/cm2
2 x 80 fs
variable delay
0 - 300 fs
Trump, Rottke and Sandner
PRA 59 (1999) 2858
Pump-probe (D2+)
v=0
0.3 PW/cm2
2 x 25 fs delay 30 fs
Norm(t)
PCE(t)
Dissociation
Laser
Coulomb explosion
PD (t)
- - - - - (Coulomb only)
b
30
(R,t ) 
zdet

2
( z, R, t ) dz
c
 zdet
25
log scale
20
Contours: jz(R,t)
15
10
c
a
5
b
0
0
20
40
60
80
100
120
140
160
180
200
a
Pump-probe (D2+)
v=0
0.3 PW/cm2
2 x 25 fs delay 50 fs
Norm(t)
PCE(t)
PD (t)
Laser
Dissociation
Coulomb explosion
- - - - - (Coulomb only)
(R,t ) 
zdet

b
2
( z, R, t ) dz
 zdet
log scale
Contours: jz(R,t)
c
b
a
c
a
Pump-probe (D2+)
v=0
0.3 PW/cm2
2 x 25 fs delay 70 fs
Norm(t)
PCE(t)
Dissociation
Laser
PD (t)
- - - - - (Coulomb only)
b
30
(R,t ) 
zdet

2
( z, R, t ) dz
c
 zdet
25
log scale
20
Contours: jz(R,t)
c
15
10
b
a
5
0
0
20
40
Coulomb explosion
60
80
100
120
140
160
180
200
a
RESULTS III
A) Single pulse (I = 0.05 – 0.5 PW/cm2, 25 fs):
vibrational state and intensity dependence
B) Pump-probe pulses (I = 0.3 PW/cm2, 25 fs):
CE-imaging of dissociating wave packets
C) Ultrashort pump-probe pulses (I = 1 PW/cm2, 5 fs):
CE-imaging of bound and dissociating wave packets
Time evolution of a coherent superposition of states
( x, t )   ak e i k t  k ( x)
k
Time dependent density matrix:

km(t )  ak am
e ikmt , km  k  m
(t )    kk  k 
2
2
k
Time average:
2
(T ) 
 kk
k
2
k
 km(t ) k m
k m


km k m
k m
e  ikmT  1
ikmT
 0 (kmT  1)
Incoherent
mixture
H2+ (km-1 = 3 … 30 fs): produced by:
Ion source: T  s

incoherent ensemble
Ultrashort laser pulse: T  5 fs

coherence effects expected
autocorrelation
D2
D2+
t
pump 1 PW/cm2 5 fs
D0 + D+
D+ + D+
probe 2 PW/cm2 5 fs
Coulomb explosion imaging of nuclear wave packets
Fragment yield Y at Ekin :
Y(Ekin) dEkin = |(R)|2 dR
1/R
Probe
Y(Ekin) = R 2 |(R)|2
Kinetic energy
Ekin (R)
d+d
|(R,t)|2
D2+
Pump

D2
initial |(R)|2
R
|(R)|2 reconstruction from CE fragment kin. energy spectra
3.0
t = 10 fs
|(R)|2
2.5
2.0
reconstructed |(R)|2
1.5
original |(R)|2
1.0
incoherent FC distr.
0.5
0.0
0
1
2
4
3
R / a.u.
moving wave packet
5
6
7
|(R)|2 reconstruction from CE fragment kin. energy spectra
3.0
t = 20 fs
|(R)|2
2.5
2.0
reconstructed |(R)|2
1.5
original |(R)|2
1.0
incoherent FC distr.
0.5
0.0
0
1
2
3
4
R / a.u.
turning point
5
6
7
|(R)|2 reconstruction from CE fragment kin. energy spectra
3.0
t = 40 fs
|(R)|2
2.5
2.0
reconstructed |(R)|2
1.5
original |(R)|2
1.0
incoherent FC distr.
0.5
0.0
0
1
2
3
4
R / a.u.
5
6
7
|(R)|2 reconstruction from CE fragment kin. energy spectra
3.0
t = 580 fs
|(R)|2
2.5
2.0
reconstructed |(R)|2
1.5
original |(R)|2
1.0
incoherent FC distr.
0.5
0.0
0
1
2
3
4
R / a.u.
5
6
7
‘revival’