Vibrational Modulation of High Harmonic Generation in SF$_{6}$*

In a recent experiment performed at JILA (N. Wagner et al, PNAS {\bf 103} 13279, 2006), a molecule is hit by two pulses: the first stimulates Raman-active vibrations while the second generates high-order harmonics. The harmonic intensity oscillates as a function of delay time between the two pulses, with oscillation frequencies equal to those of the Raman-active modes. We interpret this oscillation as a form of quantum interference between neighboring vibrational states of the molecule. Nonzero derivatives of the ionization and recombination amplitudes with respect to nuclear coordinates give the molecule some amplitude to change vibrational states during the high harmonic process. We present a theoretical description of vibrational high harmonic modulation and compare with the experimental results of Wagner {\em et al.}