Fragmentation Dynamics of H 2 + / D 2 + in Intense Ultrashort Laser Pulses
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Transcript of Fragmentation Dynamics of H 2 + / D 2 + in Intense Ultrashort Laser Pulses
Fragmentation Dynamics of H2+ / D2
+
in Intense Ultrashort Laser Pulses
U. ThummKansas State University
• Introduction
• Method of Calculation
• Results: initial vibrational state dependenceintensity dependencepump-probe study of coherent vibrational motion
B. FeuersteinT. Niederhausen
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.
Laser pulse (Ti:sapphire) 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
Dissociation and Ionization paths
g
u
0 5 10 15
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Charge resonanceenhanced ionization
1
2(3)
CE
p + p
H2+
R [a.u.]
E [
a.u.
]
Dressed potential curves(schematic)
3
1
2
0
3
1
2
0
weak field
strong field
METHOD OF CALCULATION
)(
),,(),,(3
2/ˆ)/1ˆ(2/ˆ
t
tRzeeettRz tTitVVRTitTi RlaserscezR
O
2D Crank-Nicholson split-operator propagation
2x1D model
R
z
Laser field
p p
e-
zttV
VVTRTH
laser
laserscezR
)cos()(
ˆ/1ˆˆ
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
R-dep. softening function a(R) + fixed shape parameter b = 5
a(R) adjusted to(exact) 3D pot. curve
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
2),,( ,),,(),,( tRzAvtRz
RtRzj RR
“virtual detector”: data analysis
),,(),,(),,( 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
Evolution of nuclear probability density (R,t )dissociation probability
ionization rate jz(R,t) CE probability
Kinetic energy spectra of the fragments
Time evolution of wave function and norm (on numerical grid)
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
total fragment energy [eV]
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 = 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 = 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
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
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
Branching ratio : Dissociation vs. Coulomb explosion
RESULTS II
B) Pump-probe pulses (I = 0.3 PW/cm2, 25 fs):CE-imaging of dissociating wave packets
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
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
RESULTS III
B) Pump-probe pulses (I = 0.3 PW/cm2, 25 fs):CE-imaging of dissociating wave packets
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
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:
D2+
pump 1 PW/cm2 5 fs
D2
probe 2 PW/cm2 5 fs
D0 + D+
D+ + D+
autocorrelation
Coulomb explosion imaging of nuclear wave packets
Fragment yield Y at Ekin :
Y(Ekin) dEkin = |(R)|2 dR Y(Ekin) = R 2 |(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.
= 40 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.
= 580 fs
|(R
)|2
‘revival’
|(R)|2 reconstruction from CE fragment kin. energy spectra
reconstructed |(R)|2
original |(R)|2
incoherent FC distr.