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.