The dynamics of high harmonic generation

We study the classical and quantal ionization dynamics of a one-dimensional system by strong, low-frequency electric fields with slowly varying envelopes. We show that classical ionization can be described using the principle of adiabatic invariance, if the driving frequency is sufficiently small, and that after ionization the atomic potential does not significantly alter the motion. This dynamical picture suggests that the quantal system ionizes via a sequence of tunnelling events which produce a wavepacket oscillating back and forth across the nucleus to produce high harmonics in the spectrum of radiation emitted by the accelerating electron. We further show that it is the interference between components of this wavepacket which produces both the harmonics of the field and a sharp cut-off in the spectrum, neither of which are present in the classical spectrum.