Fragmentation Dynamics of H 2 + / D 2 + in Intense Ultrashort Laser Pulses
41
Fragmentation Dynamics of H 2 + / D 2 + in Intense Ultrashort Laser Pulses B. Feuerstein* and U. Thumm Department of Physics, Kansas State University, Manhattan, KS, 66506, USA *Permanent address: MPI für Kernphysik, Heidelberg, Germany • Introduction Outline: • Method of Calculation • Results: initial vibr. state dependence intensity dependence pump-probe study of coherent vibr. motion
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Kansas State AMO PHYSICS. Results:. initial vibr. state dependence intensity dependence pump-probe study of coherent vibr. motion. Fragmentation Dynamics of H 2 + / D 2 + in Intense Ultrashort Laser Pulses. B. Feuerstein* and U. Thumm. - PowerPoint PPT Presentation
Transcript of Fragmentation Dynamics of H 2 + / D 2 + in Intense Ultrashort Laser Pulses
Fragmentation Dynamics of H2+ / D2
+
in Intense Ultrashort Laser Pulses
B. Feuerstein* and U. Thumm
Department of Physics, Kansas State University, Manhattan, KS, 66506, USA*Permanent address: MPI für Kernphysik, Heidelberg, Germany
• Introduction
Outline:
• Method of Calculation
• Results: initial vibr. state dependenceintensity dependencepump-probe study of coherent vibr. motion
Laser pulse (Ti:sapphire)
Time scalesTcycle = 2.7 fs
Tpulse = 5 -150 fs Tv=0 = 14 (20) fs
Telectr = 0.01 fs
Energies
= 1.5 eVIp = 30 eV )20ˆ(
De = 2.8 eV )2ˆ(
Length scales
= 16000 a.u. (800 nm) R0 = 2 a.u.
H2+ (D2
+)
INTRODUCTION
H2 H2+
H0 + H+ dissociation
H+ + H+ Coulomb explosion
1
1 single ionization
2
2 dissociation
3
3 enhanced ionization (CREI)
4
4 fast coulomb explosion (FCE)
Thompson et al JPB 30 (1997) 5762Posthumus et al JPB 32 (1999) L93
Most experiments: H2 initial state(except recent H2
+ experiments: Williams et al JPB 33 (2000) 2743, Sändig et al PRL 85 (2000) 4876)
50 fs
Dressed potential curves(schematic)
Dressed potential curves(schematic)
Dressed potential curves(schematic)
Dissociation and Ionization paths
Zuo, Chelkowski, BandraukPRA 48 (1993) 3837
g
u
0 5 10 15
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Charge resonanceenhanced ionization(CREI)
1
2(3)
CE
p + p
H2+
R [a.u.]
E [
a.u
.]
METHOD OF CALCULATION
R
z
Laser field
2x1D model
zttV
RV
VVTVTH
laser
nuc
lasersceznucR
)cos()(
1
ˆˆˆ
E
)t(
)t,R,z(eee)tt,R,z( tT̂it)VVVT̂(itT̂i RlaserscenuczR
3
21
21
O
2D Crank-Nicholson split-operator propagation
p p
e-
Improved soft-core Coulomb potential
2/~~
1)~(
2Rzz
azzVsce
(Kulander et al PRA 53 (1996) 2562)
Fixed softening parameter a = 1
b)R(a)R(a)b)R(a(z~)z~(Vsce
1
122
a(R) adjusted to(exact) 3D pot. curve
R-dep. softening function a(R) + fixed shape parameter b = 5
present result
} Kulander et al PRA 53 (1996) 2562
0 2 4 6 8 100
1
2
3
4
5
Dip
ole
[a.u
.]
R [a.u.]
Dipole oscillator strength for g – u transitions
dz)R;z(z)R;z(
guDipole(R)
This work (1D)
Grid: z = 0.2 a.u.; R = 0.05 a.u.
Array for 2x1D collinear non-BO wave packet propagation“virtual detector” method
z: electron coordinateR: internuclear distance
Differential data: “virtual detector”
2),,( ,),,(),,( tRzAvtRz
RtRzj RR
),,(),,(),,( tRzietRzAtRz
Coulomb explosion
),,(),( detdet tRzR
tzpR
RtRzptRp RCE
R 2),,(),( det2)(
Integration over R and binning fragment momentum distribution
),,(),( det)( tRz
Rtzp D
R
Integration over z and binning fragment momentum distribution
Dissociation
RESULTS
B) Pump-probe pulses (I = 0.3 PW/cm2, 25 fs):CE-imaging of dissociating wave packets
Time evolution of probability density (R,t) for the nuclei –CE channel is indicated by the ionization rate jz(R,t)
Kinetic energy spectra of the fragments
Integrated data: time evolution of norm and fragmentationprobabilities (dissociation and CE)
A) Single pulse (I = 0.05 – 0.5 PW/cm2, 25 fs):vibrational state and intensity dependence
C) Ultrashort pump-probe pulses (I = 1 PW/cm2, 5 fs):CE-imaging of bound and dissociating wave packets
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
v = 40.2 PW/cm2
25 fs
Norm(t)
PD (t)
PCE(t)
dztRzR,tz
z
det
det
2),,()(
log scale
a
a
b
b
c cdd
Dissociation
1
2(3) V 0
V 50 2 4 6 8 1019
19
Coulomb explosion
- - - - - (Coulomb energy)
Contours: jz(R,t)
Laser
v = 00.2 PW/cm2
25 fs
Dissociation Coulomb explosion
1
2(3) V 0
V 50 2 4 6 8 1019
19
- - - - - (Coulomb energy)
dztRzR,tz
z
det
det
2),,()(
log scale
Norm(t)
PD (t) PCE(t)Laser
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
v = 10.2 PW/cm2
25 fs
Dissociation
1
2(3) V 0
V 50 2 4 6 8 1019
19
Coulomb explosion
- - - - - (Coulomb energy)
dztRzR,tz
z
det
det
2),,()(
log scale
Contours: jz(R,t)
Norm(t)
PD (t)
PCE(t)Laser
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
v = 20.2 PW/cm2
25 fs
Dissociation Coulomb explosion
1
2(3) V 0
V 50 2 4 6 8 1019
19
- - - - - (Coulomb energy)
dztRzR,tz
z
det
det
2),,()(
log scale
Contours: jz(R,t)
Norm(t)
PD (t)
PCE(t)
Laser
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
v = 30.2 PW/cm2
25 fs
Dissociation Coulomb explosion
1
2(3) V 0
V 50 2 4 6 8 1019
19
- - - - - (Coulomb energy)
dztRzR,tz
z
det
det
2),,()(
log scale
Contours: jz(R,t)
Norm(t)
PD (t)
PCE(t)
Laser
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
v = 40.2 PW/cm2
25 fs
Norm(t)
PD (t)
PCE(t)
dztRzR,tz
z
det
det
2),,()(
log scale
a
a
b
b
c cdd
Dissociation
1
2(3) V 0
V 50 2 4 6 8 1019
19
Coulomb explosion
- - - - - (Coulomb energy)
Contours: jz(R,t)
Laser
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
v = 50.2 PW/cm2
25 fs
Dissociation Coulomb explosion
1
2(3) V 0
V 50 2 4 6 8 1019
19
- - - - - (Coulomb energy)
dztRzR,tz
z
det
det
2),,()(
log scale
Contours: jz(R,t)
Norm(t)PD (t)
PCE(t)
Laser
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
Dissociation Coulomb explosion
1
2(3) V 0
V 50 2 4 6 8 1019
19
- - - - - (Coulomb energy)
v = 60.2 PW/cm2
25 fs
dztRzR,tz
z
det
det
2),,()(
log scale
Contours: jz(R,t)
Norm(t)PD (t)
PCE(t)
Laser
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
Dissociation Coulomb explosion
1
2(3) V 0
V 50 2 4 6 8 1019
19
- - - - - (Coulomb energy)
v = 70.2 PW/cm2
25 fs
dztRzR,tz
z
det
det
2),,()(
log scale
Contours: jz(R,t)
Norm(t) PD (t)
PCE(t)
Laser
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
v = 80.2 PW/cm2
25 fs
Dissociation Coulomb explosion
1
2(3) V 0
V 50 2 4 6 8 1019
19
- - - - - (Coulomb energy)
dztRzR,tz
z
det
det
2),,()(
log scale
Contours: jz(R,t)
Norm(t) PD (t)
PCE(t)
Laser
v = 3 v = 6
3
1
2
0
0.05 PW/cm2 0.1 PW/cm2
0.5 PW/cm20.2 PW/cm2
12
12
12
12
0 5 100.0
0.2
0.4
0.6
0.8
E / eV0 5 10
0.0
0.2
0.4
0.6
0.80.05 PW/cm2 0.1 PW/cm2
0.5 PW/cm20.2 PW/cm2
12
12
12
12
0 5 100.0
0.2
0.4
0.6
0.8
E / eV0 5 10
0
1
2
3
0.1 1
0.01
0.1
1
Pro
babili
ty
Intensity / (PW/cm2)
Pump-probe experiment
Trump, Rottke and SandnerPRA 59 (1999) 2858
1
2(3) CE
D2 target
0.1 PW/cm2
2 x 80 fs
variable delay0 - 300 fs
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
dztRzR,tz
z
det
det
2),,()(
log scale
Contours: jz(R,t)
Pump-probe (D2+)
v = 00.3 PW/cm2
2 x 25 fs delay 30 fs
Dissociation Coulomb explosion
- - - - - (Coulomb only)
Norm(t)
PD (t)
PCE(t)
Laser
a
a
b
b
c
c
Dissociation Coulomb explosion
- - - - - (Coulomb only)
Pump-probe (D2+)
v = 00.3 PW/cm2
2 x 25 fs delay 50 fs
Norm(t)
PD (t)
PCE(t)
Laser
ab
c
a
b
cdztRzR,t
z
z
det
det
2),,()(
log scale
Contours: jz(R,t)
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
Dissociation Coulomb explosion
- - - - - (Coulomb only)
Pump-probe (D2+)
v = 00.3 PW/cm2
2 x 25 fs delay 70 fs
Norm(t)
PD (t)
PCE(t)
Laser
a
b
cdztRzR,t
z
z
det
det
2),,()(
log scale
Contours: jz(R,t)
ab
c
Time evolution of a coherent superposition of states
)(),( xeatxk
kti
kk
mkkmti
mkkmkmeaat ,)(
Time dependent density matrix:
2)(t
mk
mkkm t )(2
kkkk
Time average:
)1(0 TkmIncoherentmixture
2)(T
2k
kkk Ti
e
km
Ti
mkmkkm
km
1
Ion source: T s incoherent ensemble
Ultrashort laser pulse: T 5 fs coherence effects expected
H2+ (km
-1 = 3 … 30 fs): produced by:
pump 1 PW/cm2 5 fs
D2+
D2
probe 2 PW/cm2 5 fs
D0 + D+
H+ + H+
autocorrelation
Coulomb explosion imaging of nuclear wave packets
Fragment yield Y at Ekin :
Y(Ekin) dEkin = |(R)|2 dR Y(Ekin) = R2 |(R)|2
R
Kinetic energy Ekin (R)
|(R,t)|2
initial |(R)|2
Pump
Probe
1/R
D2+
D2
d + d
0 1 2 3 4 5 6 70.0
0.5
1.0
1.5
2.0
2.5
3.0
R / a.u.
= 10 fs
|(R
)|2
|(R)|2 reconstruction from CE fragment kin. energy spectra
reconstructed |(R)|2
original |(R)|2
incoherent FC distr.
moving wave packet
0 1 2 3 4 5 6 70.0
0.5
1.0
1.5
2.0
2.5
3.0
R / a.u.
= 20 fs
|(R
)|2
turning point
|(R)|2 reconstruction from CE fragment kin. energy spectra
reconstructed |(R)|2
original |(R)|2
incoherent FC distr.
0 1 2 3 4 5 6 70.0
0.5
1.0
1.5
2.0
2.5
3.0
R / a.u.
= 30 fs
|(R
)|2
|(R)|2 reconstruction from CE fragment kin. energy spectra
reconstructed |(R)|2
original |(R)|2
incoherent FC distr.
0 1 2 3 4 5 6 70.0
0.5
1.0
1.5
2.0
2.5
3.0
R / a.u.
= 40 fs
|(R
)|2
|(R)|2 reconstruction from CE fragment kin. energy spectra
reconstructed |(R)|2
original |(R)|2
incoherent FC distr.
‘collapse’
|(R)|2 reconstruction from CE fragment kin. energy spectra
reconstructed |(R)|2
original |(R)|2
incoherent FC distr.
0 1 2 3 4 5 6 70.0
0.5
1.0
1.5
2.0
2.5
3.0
R / a.u.
= 165 fs
|(R
)|2
0 1 2 3 4 5 6 70.0
0.5
1.0
1.5
2.0
2.5
3.0
R / a.u.
= 580 fs
|(R
)|2
‘revival’
|(R)|2 reconstruction from CE fragment kin. energy spectra
reconstructed |(R)|2
original |(R)|2
incoherent FC distr.
WHAT’S NEXT ?
• Lasser-assisted collisions
• More on time-resolved nuclear dynamics: decoherence and revivals
• Add degrees of freedom: 2D (electron) + 1D(R) H2 : 2 x 1D (electrons) + 1D(R)
Thumm Group:
B.F.:
GOES BACK TO EXPERIMENT!(Good Bye, Theory)
