1. 18th International Laser Physics Workshop
Theoretical and experimental progress towards HHG and quantum tomography of excited states of molecules
George N. Gibson
University of Connecticut
Department of Physics, and
The Institute of Photonic Sciences
with Jens Biegert
Grad student:
Li Fang
Funding:
NSF-AMO
July 14, 2009
18th International Laser Physics Workshop
Barcelona, Spain

2. Introduction
Interested in QT of excited states of molecules – can watch bonds break or evolve in time.

3. Problems with Quantum Tomography
Inner-orbital ionization, or role of HOMO-1
Greater variety of orbital symmetries – can they be reconstructed? sg su pu sg sg pg

4. Evidence for inner-orbital ionization has been around for awhile
Generally hard to detect in ion TOF.
Electron spectroscopy on N2.
All charge-asymmetric channels
New data on populating A-state in I2+
Ionization of B-state to (2,0) asymmetric state – even excited states experience inner-orbital ionization!

5. Photo-electron Spectroscopy
X-state: 4 photons
A and B states: 5 photons
[PRL 67, 1230 (1991)]

6. Charge asymmetric dissociation
I24+ → I2+ + I2+ or I3+ + I1+
The branching ratio to the asymmetric channel can be 20%. [PRA 58, 4723, (1998)]

7. I2 potential energy curves
Asymmetric channels probably populated through inner-orbital ionization.

8. I2+ pump-probe data

9. (2,0) vibrational signal
Amplitude of vibrations so large that we can measure changes in KER, besides the signal strength. [PRA, 75, (2007)]
Know final state – want to identify intermediate state.

10. I2 potential energy curves

11. What about the dynamics?
How is the A-state populated?
I2  I2+  (I2+)* - resonant excitation?
I2  (I2+)* directly – innershell ionization?
No resonant transition from X to A state in I2+.

12. From polarization studies
The A state is only produced with the field perpendicular to the molecular axis. This is opposite to most other examples of strong field ionization in molecules.
The A state only ionizes to the (2,0) state!? Usually, there is a branching ratio between the (1,1) and (2,0) states, but what is the orbital structure of (2,0)?
Ionization of A to (2,0) stronger with parallel polarization.

13. Implications for HHG and QT
We can readily see ionization from orbitals besides the HOMO.
Admixture of HOMO-1 depends on angle.

14. Wavelength-dependent pump probe scheme
Change inner and outer turning points of the wave packet by tuning the coupling wavelength.
Femtosecond laser pulses:
Pump pulse: variable wavelength. (517 nm, 560 nm and 600 nm.) Probe pulse: 800 nm.

15. Can ionize from the B state to the (2,0) asymmetric state.
I2+ spectrum: vibrations in signal strength and kinetic energy release (KER) for different pump pulse wavelength [517nm, 560 nm and 600 nm]
Can ionize from the B state to the (2,0) asymmetric state.

16. What about orbital reconstruction? [PRA 78, 033423 (2008)]
Assume that the 3-step model for HHG gives us exactly what we want:
This has the right form for a Radon transformation,
allowing tomographic reconstruction.

17. However, we don’t want:
So, we consider the length and velocity gauges:

18. Length vs. velocity forms
Using the length form, we recover: this is useful, because we know r.
Similarly, in the velocity form, we recover: This is actually easier to deal with, since there is no division by zero, and generally gives better results.

19. Assume two forms are equal:
Calculate right-hand side and perform inverse Radon transformation to recover

20. 1g ground state

21. Radon xforms – parallel 1ssg
Pseudo-radon: acceleration
Proper-radon: acceleration
Proper-radon: velocity
Proper-radon: length

22. 1u – excited state

23. Radon xforms – parallel 1ssu
Pseudo-radon: acceleration
Proper-radon: acceleration
Proper-radon: velocity
Proper-radon: length

24. Radon xforms – perp. 1ssu Pseudo-radon: acceleration
Proper-radon: acceleration
Proper-radon: velocity
Proper-radon: length

25. 1u – excited state

26. 1g – excited state

27. Conclusions
Velocity form may be better for actual reconstruction of orbitals
Some symmetries are very hard to reconstruct, especially g.
Perpendicular polarization in the molecular frame gives the best results.

28. Coordinate system

29. Ionization geometry

30. Ionization geometry