QED THEORY OF HARMONIC EMISSION BY A STRONGLY DRIVEN ATOM

We present a theory of harmonic generation by a strongly driven atom w ithin the framework of non-relativistic QED. The atom is assumed to po ssess a finite number N of levels and ionization is neglected. This at om is dressed by the driving field using a unitary time-dependent tran sformation. Within the quasistatic approximation this transformation i s shown to lead from the bare to the Floquet atom. The interaction of the Floquet atom with the vacuum modes is derived and it is shown to g ive rise both to the high-order harmonic and to the hyper-Raman spectr um. In the case N = 2 the spectrum of the light scattered into the vac uum modes can be evaluated analytically and it is shown to consist of two parts. Neglecting interference between these two parts, the first of them is the high-order harmonic spectrum displaying peaks at the od d harmonics of the driving field. The second part is the hyper-Raman s pectrum which has finite bandwidth and which displays peaks at the eve n harmonics of the laser frequency, centred at the Stark-shifted natur al atomic frequency. These two spectra partially overlap and they are discussed in various ranges of intensity of the driving field, both in the minimal coupling and in the multipolar scheme. The results suppor t recent suggestions that the presence of the plateau is related to in terference between the two spectra. The dependence of the high-order h armonic spectrum from the driving field intensity is found to be relat ed to that of the hyper-Raman spectrum in such a way that when the for mer increases the latter decreases and vice versa. It is argued that t his might help to explain the non-visibility of the hyper-Raman lines when the high-order harmonics are visible.