Transitions between stationary states of the electron-photon field system: A new mechanism for interpreting high optical field phenomena

Optical transitions between stationary states of the electron-photon field system, known as quantum Volkov states, offer a new framework within which to interpret a rich variety of phenomena observed in intense optical fields. In this view, photons and electrons interact to form transient complexes which are capable of annihilating fundamental photons to produce more energetic radiation, or releasing photons back to the optical field. That is, they mediate the exchange of energy between the fundamental and secondary optical fields. The application of this new picture, which has no classical analog, to high harmonic generation is reviewed here. In previous publications [J. Gao, F. Shen, and J. G. Eden, Phys. Rev. Lett. 81, 1833 (1998); J. Phys. B32, 4153 (1999); Phys. Rev. A61, 043812 (2000)], theoretical predictions of harmonic spectra and the polarization characteristics of individual harmonics have been compared with semiclassical calculations and experiment and several key results are summarized here. Specifically, an analytic expression for the harmonic generation transition matrix element has been derived that is valid for an arbitrary polarization of the fundamental optical field and is in agreement with the experimental data in the literature. Also, recent calculations of the spectral lineshapes of individual harmonics are presented here and compared with published measurements. QED theory predicts that the harmonic linewidth is essentially independent of the fundamental intensity when the ponderomotive potential is less than the atomic ionization potential but increases rapidly at higher intensities. The implications of these results for future experiments are also discussed.