Vibrational Modulation of High Harmonic Generation in Molecules

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Vibrational Modulation of High Harmonic
Generation in Molecules

• Zach Walters, Stefano Tonzani, Chris H. Greene

Funding Department of Energy, Office of Science
and NSF EUV ERC
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-Excite molecules at t0 using a perturbative
weak Raman pulse, which excites the 3
Raman-active vibrational modes of SF6. -Then
wait a time T, and hit the molecule with a strong
pulse that ionizes and generates a high harmonic
photon (39th in this case)
Wagner et al., PNAS 103 13279
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Wagner et al. PNAS 103 13279
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6 vibrational normal modes of SF6, taken from
Wagner et al. PNAS 103 13279
Raman active modes 1,2,5
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Whats going on here?

• 3 step model electrons tunnel ionize, are
  accelerated by the strong laser field, and
  recombine with their source atom/molecule all
  are electronic processes, and all happen much
  faster than the vibrational timescale.
• But in varying the time delay between pump and
  probe, youre changing the vibrational degree of
  freedom.
• So there has to be some interplay between the
  electronic process and the vibrational state.

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Vibrational/Electronic Interaction

• The molecule can hop between adjacent vibrational
  states during Ionization or Recombination.
• This hopping means that different vibrational
  states can interfere with one another.

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Finally, the molecular ion evolves between
ionization and recombination. We calculate the 3
lowest adiabatic energies at various
displacements to find potential energy curves
near the conical intersection.
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High Harmonic Generation acts like a Molecular
Beamsplitter
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Electron Propagation

• Semiclassical propagator electrons follow all
  classical trajectories, picking up phase as they
  do so
• Most of these trajectories miss the molecule.
• Scattering from the molecular ion is complicated!

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e-scattering wavefunctions - Adenine
2.2 eV
2.6 eV
Similar to 1st and 2nd virtual orbitals
(Tonzani and CHG, 2006 J. Chem. Phys.)
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SF6 Virtual Orbital at 1.5 Hartree (39th
harmonic scattering energy)
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Semiclassical Propagation

• Ionization Unperturbed HOMO in allowed region,
  WKB exponential in tunneling region, trajectories
  leave from outer turning surface
• Recombination semiclassical trajectories project
  onto electron-molecule scattering states
• Stationary phase trajectories start with zero
  velocity, return normal to surface with energy
  equal to scattering state energy

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Comparison Between Theory and Experiment
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Summary

• Interference between adjacent vibrational states
  causes the intensity modulation observed in the
  JILA experiment.
• This model easily extends to more complicated
  vibrational motion and molecular wavefunctions.
• Preprint http//arxiv.org/abs/physics/0701113