Interpretation of high-order harmonic generation in terms of transitions between quantum Volkov states

A theoretical perspective of high-order harmonic generation is presented in which transitions between quantum Volkov states\char22{}stationary solutions to Schr\"odinger's equation for an electron interacting with a quantized optical field\char22{}are the dominant mechanism for producing radiation. The picture proposed here is one in which the interaction of an intense optical field with an electron forms a photon-electron ``quasiatom'' and the stationary states of this complex can be viewed as the high optical field analog of bound states of an atom. Consequently, although momentum conservation for the overall harmonic generation process requires that an electron eventually return to the parent atom, the electron and fundamental optical field are treated as an isolated system with well-defined energy and momentum. To introduce a secondary photon (harmonic) field, the matrix element describing the electron-photon field interaction through quantum Volkov states is modified in a perturbative manner. The result is the production of harmonic photons by Volko$\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$Volkov-state transitions, a process which has no classical counterpart. The generation of odd harmonics of the fundamental field and the requirement that the final state of the electron be the initial bound state of the atom follow directly from the theory. A clear connection between harmonic generation and above-threshold ionization (ATI) is drawn by maintaining the discrete, nonzero energies of photoelectrons injected into the driving optical field by ATI. For experiments in which the laser pulse width is \ensuremath{\gtrsim}100\char21{}150 fs, only the lowest ATI photoelectron orders contribute significantly to harmonic generation, whereas higher-energy electrons escape from the parent atom during the pulse risetime. As the duration of the fundamental field is decreased, however, the rapid rise of the field intensity to its peak value effectively traps more energetic photoelectrons, thereby extending the harmonic response to shorter wavelengths. An analytic expression for the transition matrix for the harmonic generation process is derived and is compared with the predictions of semiclassical theory and published experimental results, including harmonic spectra and polarization data.