Transcript High Harmonic Generation in Molecules

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
-Excite molecules at t=0 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
Wagner et al. PNAS 103 13279
6 vibrational normal modes of SF6, taken from Wagner et al. PNAS 103 13279
Raman active
modes 1,2,5
What’s going on here?
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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, you’re
changing the vibrational degree of
freedom.
So there has to be some interplay
between the electronic process and
the vibrational state.
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.
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.
High Harmonic Generation acts like a
Molecular Beamsplitter
2 Types of Interferometry
Known mixing,
unknown wavefunction
Known wavefunction,
Unknown mixing
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!
e-scattering wavefunctions Adenine
2.2 eV
Similar to 1st and 2nd virtual orbitals
2.6 eV
(Tonzani and CHG, 2006 J. Chem. Phys.)
SF6+ Virtual Orbital at 1.5 Hartree
(39th harmonic scattering energy)
Semiclassical Propagation
• Ionization: Unperturbed HOMO in
allowed region, WKB exponential
in tunneling region, trajectories
leave from outer turning surface
• Recombination: semiclassical
trajectories project onto electronmolecule scattering states
• Stationary phase trajectories start
with zero velocity, return normal
to surface with energy equal to
scattering state energy
Comparison Between Theory and
Experiment
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