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)