1. Watching the Time Evolution of Wave-Packets in Diatomic Molecules
Birte Ulrich
Thank you igor , Hi my name is…, I have been here for almost a year working with prof. lew cocke and company, doing research on laser ionization of atoms and molecules as part of my diploma thesis, so I am a diploma student, and please bear this in mind for your questions…..hahah
Today I will be talking about how we can observe the molecular wave packet motion in diatomic molecules starting with the simplest molecules H2 and extending to molecules like o2.

2. Outline:
• Double ionization of molecules and the production of higher charge states
• Dissociation and CREI with long laser pulses
• COLTRIMS technique
• Technical improvements on the chamber
• Pump-probe experiments with H2, D2 and O2
• Molecular wave packet motion in H2
• Molecular wave packet motion in O2
• Summary
This is the outline of my talk, First I will talk about the double ionization of molecules and how their kinetic energy release depends on the pulse duration. This arises the question how higher charge states are produced out of doubly charged molecules.
One important aspect of my talk will be the dissociation and the charged resonance enhanced ionization of molecules, which is crucial for the ionization in long laser pulses.
I will say something about the spectroscopy technique we are using to measure the fragments of out diatomic gases. Before we could start with the real experiment we had to improve some technical things on our chamber, which made the final experiments possible.
Finally I will present the results of our pump-probe experiments on H2, D2 and O2.. With our pump probe set-up we are able to take data which shows the motion of a molecular wave packet.
At the end I will give a summary of our results.

3. Kinetic energy release for double ionization of O2 for
short and long pulse high intensity
Short pulse “freezes” the nuclear motion
Coulomb explosion from smaller
internuclear distances lead to higher kinetic energy release
short pulse
Long pulse let the molecule dissociate
before it Coulomb explodes
long pulse
This is a comparison of two kinetic energy spectra for O2 with short and long pulse high intensity. At high intensities, the spectrum for short pulse shows higher kinetic energy release and more structure than the spectrum for long pulse.
The higher kinetic energy release for short pulse is due to the fact, that the molecule ionizes at smaller internuclear distance, which leads to a higher energy release when it Coulomb explodes. The short pulse doesn’t give the molecule much time to move before it ionize.
The different peaks are coming from different excited state which are populated in O2+ before the removal of the second electron.
In the long pulse spectrum there is just one main peak remaining. Here the molecule has enough time to dissociate before it Coulomb explodes. Thus it has a smaller kinetic energy release., and we wanted to understand if this is simialt to H2 where CREI dominate when h2 ionized by high-intensity long pulses..
KER from Coincidence O+ + O+

4. Looking at higher charge states
How will higher charged molecules
ionize, which almost certainly evolve
from doubly charged molecules?
My first project was to look at the higher charge states of O2 and N2.
The question was, whether the production of higher charge >3, states also exhibit similar behavior as the doubly- charged and how they are connected? In terms of dependence on the pulse duration and the intensity of the laser?
I will come back to this question later on in my talk.

5. H2+ Enhanced Ionization time
A very crucial ionization mechanism for the understanding of my experiments is the enhanced ionization. In the first step a Hydrogen molecule is singly ionized to the 1s sigma g potential curve. Here the molecule dissociate when the electron is moving out of the potential well. Finally the molecule double ionizes. The theory predicts two critical distances where the ionization rate is enhanced. These are around 7 a.u. and 10 a.u.
This can be understood if we look at the nuclear potentials of the H2+ molecule.
When the protons are very close to each other the probability for the electron to be bond either here… or here… is high. When the protons are far from each other the barrier between them decrease the probability for the electron to free. But when the protons reach certain distance
the remaining electron can free easily. I will come back to the CREI concept when I show my results…
Theory predicted two maxima in the ionization rates at critical distances:
Rc~7 a.u and Rc~10 a.u. ??!!!

6. COLD Target Recoil Ion Momentum Spectroscopy
This is our experimental set up. We use COLTRIMS to measure the ions coming from the diatomic molecules. COLTRIMS stands for COLD Target Ion Momentum Spectroscopy.
We focus the laser with a spherical mirror on a supersonic gasjet. The ions produced in the interaction region are projected by a electric field on a multi channel plate followed by a time position sensitive anode. The times are converted to momentums of the ion.
The laser we use is a Ti:sahirre laser with a repetition rate of 1000Hz and a wave length of 800nm.
repetition rate: 1000 Hz
wave length: 800 nm
Laser-Polarization

7. Problems: Experiments with very high intensities caused an
immense count rate and made the analysis impossible.
Solution: Piezoelectrical slits to make the jet thinner.
Thus a lower count rate would make it possible to run
with higher intensities.
Before we could start with the real experiment we had to make some improvements on our gas jet. The problem was, that very high intensities caused an immense counting rate and our spectra were full of random coincidences. This made the analysis extreme slow the results for high intensities unusefull. The solution was to put piezoelectrical slits in our chamber to make the jet thinner and run with lower count rates and even higher intensities.
The only limiting factor would be the background of our chamber. At one point, when the jet is very thin, we would have more counts coming from the background than from the jet.
Limiting factor: The background in the chamber will limit the thickness
of the jet.

8. cut by piezoelectrical slits from 1.5mm down to 50 μm jet
Scanning of the laser focus for different jet sizes by changing the position of the spherical mirror
spherical mirror
laser
moved by a
manipulator
laser focus
The new slits made it possible for us to scan the laser focus for different jet sizes.
This picture shows a contour plot for the intensity distribution in the laser focus. The highest intensity is in the Rayleigh range. The red line marks where the intensity reaches ½ of the maximal intensity. Here the production of higher charge states is enhanced in comparison to the production of lower charge states.
The z-axis lies in the laser propagation an the Jet it perpendicular to it.
With our piezoelectrical slits we can cut our jet from 1.5mm down to 50microns. Moving the spherical mirror with a manipulator we shift the laser focus in and out of the gas jet. With a jet size thinner than the Rayleigh length we can see how the ratio between double to single ionization improve. We start at -1 (which is out of the focus) and go to 1 (which is out of the focus again). …
A jet thinner than the Rayleigh length
makes it possible to enhance the
production of higher charge states in comparison to lower charge states
Saturation
Ar2+

9. Optimization of the ratio of Ar2+/Ar+ by scanning the laser focus
Out of the jet -1
Out of the jet 1
And here are the results for Ar.
First we see just background. The water peak is the stongest peak in this time of flight…
Than we move the laser focus in the jet and see the ratio af Ar 2+ and Ar+ improving…
The next slice is in the focus of the laser and gives us the best ratio of Ar2+ to Ar+…
Finally we are going out of the jet again till we see the water peak the strongest feature.

10. Jet Thickness:1.5 mm Jet Thickness:50 μm
Comparison between data taken with a jet thickness of
1.5 mm and around 50μm
O2 long pulse, intensity 9.2 x1014 W/cm2 Count rate 15000
O2 long pulse, intensity x Count rate 1100
O++O+
O++O+
O++O+
O++O2+
O++O2+
O++O3+
This is a comparison between data taken with a 1.5 mm gas jet and a 50micron jet. The count rate with a big jet size is huge and the spectrum is full of randoms.
While the spectrum with a thin jet is clean and the coincidence lines of the higher charges molecules are clearly to see.
O++O2+
O2++O+
O3++O+
O2++O2+
O2++O2+
O2++O+
O2++O+
O2++O2+
O3++O2+
O2++O3+
tof2 vs tof1
tof2 vs tof1
Jet Thickness:1.5 mm
Jet Thickness:50 μm

11. Higher charge states with long pulse and short
pulse high intensity
N++N+
N++N2+
N2++N+
N++N+
N++N2+
N2++N+
N2++N2+
N3++N+
N2++N3+
N3++N3+
N3++N2+
N++N+
After this improvement we could start looking at higher charge states of Oxygen and Nitrogen in dependence of pulse duration and intensity. These are two coincidence spectra with approximately the same intensity for long and short pulse. The left spectra is for short pulse and the right is for long pulse
On the x-axis is the time of the first particle and on the y-axis the time for the second particle. When to particles coming exacty from the same molecule they will lay on these… coincidence lines.
We can see that for the same intensity we create up to N6+ with long pulse, but just N3+ with short pulse. The question is how are higher charge states produced and is there production due to a CREI like ionization mechanism?
The idea now was to do pump probe experiments to excite the molecule with a weak pump pulse to singly ionize it and to probe it with a strong probe pulse and get higher charge states. So the molecule has enough time to move.
tof2 vs tof1
tof2 vs tof1
But: No higher charge states with short pulse (8fs) very high intensity.
Does a CREI like ionization mechanism lead to higher charge states?

12. Pump-Probe Setup d d d
Pump pulse d
pump-pulse
Probe pulse
probe-pulse θ d
This is our pump probe set up. It consists of two pieces of glas. One small round piece and one big piece which has a hole in it. The small piece seems to be cut out of the big piece. The part of the pulse which goes through the small piece and the hole is the pump pulse. The part of the laser which goes through the big piece is the probe pulse.
If the pieces are alined exactly parallel both pulses need the same time to travel to the chamber. A rotation of the big peace will generate a delay between the two pulses. Since the probe pulse has to travel a longer distance in the glas he weill arrive a few femtosecond later than the pump pulse. The delay between the to pulses depends on the angle theta. This pump-probe experiment makes it possible to take data in one femtosecond steps from 0 to 100fs delay. The big peace is moved by a small motor and can be controlled by our data acquisition system. d
Pump probe goes through a medium of thickness d, while probe pulse pass a thickness x.
x > d → time delay between the pulses in dependence on the angle θ.
pump-pulse θ x
probe-pulse

13. H2 Potential curves pump pulse: intensity 1*1014 W/cm2 single ionizes
probe pulse: intensity 1*1015 W/cm2
double ionizes
This is how we expect to ionize our H2 molecule with our pump probe setup. The first weak pump pulse single ionize the molecule to the 1s sigma g curve. The wave packet starts moving and reaches after 12fs second the outer turning point. Here it can go out and dissociate the molecule. The second pulse which is much stronger double ionizes the molecule.
With higher intensity it is also possible to ionize the H2+ without dissociating it directly from the 1sigma g curve. In this case the kinetic energy release will be higher.
The intesities of our pulses are approximately 1014 W/cm2 for the pump pulse and 1015 W/cm2 for the probe pulse.

14. H2 Vibrational Packet u g g: ionization u: dissociation
This movie from Xiao-Min shows the vibrational wave packet in the sigma g and sigma u potential curves.
In the sigma u curve you see the oscillation of the wave packet and in the sigma u curve you can see the dissociation.
g: ionization
u: dissociation
Pump: 8 fs 1014 W/cm2
Model: Xiao-Min Tong ,C.D.Lin

15. Pump-Probe for H2 data after background subtraction
Oscillation of wave packet on
the 1σg potential
data after background subtraction
This are our results for H2.. The KER spectrum in dependence of the delay between pump and probe shows two main features. We observe the oscillation on the 1sigma g potential curve, which is the red curve. With this intensity this ionization process seems to be dominant.
We also see sequential ionization on the 1 sigma u potential curve. This ionization process starts with approximately 15 fs delay, which is due to the fact that the wave packet need time to dissociate.
To make our data cleaner we do background subtraction. We take a delay range from 0 to 10fs and averaging the counts for each kinetic energy. Since the two pulses overlap at this delay, we should not have any features coming from the pump probe experiment. Subtracting this slice multiplied by a factor from the hole spectra will enhance the structure coming from the pump probe itself. The oscillation is now easier to see.
Sequential ionization on 1σu potential curve

16. Model for the Kinetic Energy Release
Comparison calculation and experiment
assumptions: 5.2 a.u. internuclear
distance for the electron to
free.
12fs time it takes the wave
packet to reach the outer
turning point.
This is a model to calculate the kinetic energy release for the sequential ionization on the 2pi sigma u curve.
Starting at an internuclear distance of 5 a.u. where the electron gets free we calculate the energy of the potential curve in dependence of the internuclear distance. The internuclear distance R itself depends on the time. Starting with a delay time of 12 fs, which is the time the wave packet needs to reach the outer turning point, we model the molecule’ s movement.
To get the kinetic energy release we take the difference between the energy the molecule has when dissociate in the 2p sigma u curve and it has at a certain delay time. To this energy we also have to add the energy release from the Coulomb curve which 1/R.
The comparison with the experiment shows a good agreement.

17. Pump probe for D2 – with weaker probe pulse
Pump probe with lower
intensity enables the
Observation of
CREI features.
This are results for d2 with weaker probe pulse. A lower intensity enhances the features for CREI. Here the molecule dissociates before it ionizes. We see to main peaks at around 5 eV. By subtracting the energy release coming from the dissociation we can calculate the internuclear distance. By using the relation between r and the kinetic energy for Coulomb explosion, we get a value around 5.3 a.u. R1 R2

18. H2+ Enhanced Ionization time
A very crucial ionization mechanism for the understanding of my experiments is the enhanced ionization. In the first step a Hydrogen molecule is singly ionized to the 1s sigma g potential curve. Here the molecule dissociate when the electron is moving out of the potential well. Finally the molecule double ionizes. The theory predicts two critical distances where the ionization rate is enhanced. These are around 7 a.u. and 10 a.u.
This can be understood if we look at the nuclear potentials of the H2+ molecule.
When the protons are very close to each other the probability for the electron to be bond either here… or here… is high. When the protons are far from each other the barrier between decrease the probability for the electron to free. But when the protons reach certain distance
the remaining electron an free easily. I will come back to the CREI concept when I show my result…
Theory predicted two maxima in the ionization rates at critical distances:
Rc~7 a.u and Rc~10 a.u. ??!!!
But we always found in our experiments with the long pulse that the CREI position may shift as the laser intensity increases..

19. Comparison with the theory
This is the comparison between the experiment and the calculation from Xiao-Min.
calculation: Xiao-Min Tong, C.D. Lin
8 fs, 2x1015 W/cm2

20. Pump-Probe for O2 O22+ probe O2+ pump O2
Oscillation of wave packet(s) in bond
potential
X2πg
2Σu
O2+
W3Δu
B3Σu- O2
pump
probe
O22+
The pump probe experiments for Oxygen are showing similar features like we observe with hydgrogen. We see oscillation of wave packets in bond potentials and sequential ionization from dissociation curve. But we do not yet understand which potential curves are involved in the ionization process.
Sequential ionization on dissociation
curve

21. 1-D Display of the KER for Oxygen for pump probe
1-D Display of the KER for Oxygen for pump probe with different time delays
Higher kinetic energy release
due to smaller internuclear
distances.
small delays
This is a one dimentional display of the kinetic energy release for Oxygen with different time delays. For smaller delays we observe higher kinetic energy release and more structure in the energy release. This is due to ionization at smaller internuclear distances. The different peaks are coming from different excited state which are populated in O2+ before the removal of the second electron.
When we go to higher delays the sequential ionization on the dissociation potential curve seems to be the dominant prosess for ionization.
On could say, that the kinetic energy release of higher delays has similar structures like the KER of a normal long pulse.
higher delays
KER from Coincidence O+ + O+

22. Summary: Oscillation of the wave packet in 1σg potential and
• H2 shows two features evolving with the delay:
Oscillation of the wave packet in 1σg potential and
sequential ionization on the 1σu potential curve.
• O2 shows similar features like H2, but it is not yet
understood which potentials are involved in the
ionization process.
Pump-probe experiments on O2 with higher delays would
be interesting to see, how the ionization process evolve.

23. Time of flight for O2