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Grad student: Li Fang Funding : NSF-AMO

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

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Grad student: Li Fang Funding : NSF-AMO

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  1. 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, 063410 (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. 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

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