Two-photon excitation of atoms by ultrashort electromagnetic pulses in a discrete spectrum

Abstract

The development of methods of generation of ultrashort pulses (USP) of femto-and attosecond duration ranges with controlled parameters necessitates the theoretical study of features of their interaction with a matter [1]. Among such features that do not exist in case of "long" pulses should first of all be the nonlinear dependence of the photoprocess probability W on the USP duration () [2] as well as the dependence on the carrier phase with respect to the pulse envelope () [3][4]. It should be noted that if the dependence of the probability W on the phase  manifests itself either only for very short pulses, when  < 1 ( is carrier frequency of the pulse), or in case of a nonlinear photoprocess [3], the function W() can differ from a linear function in the limit  > 1 too for fields of moderate strength, when the perturbation theory isTo describe photoprocesses in an USP field, various theoretical methods were used. Thus in the works of V.I. Matveev with co-authors [5-7] the sudden perturbation approximation was used to describe scattering of attosecond pulses by different quantum systems: atoms, ions, molecules, and clusters. In the V.P. Krainov's papers [8][9], excitation of a two-level system under the USP action was studied with the use of solution of the Schrödinger equation, and photoionization of atoms was calculated both within the framework of the perturbation theory[10] and in the Landau-Dykhne approximation [11]. In the latter work it was shown in particular that ionization of an atom by an intense single-cycle cosine pulse is much more efficient than under the action of a sine pulse.In the paper [12], within the framework of the perturbation theory the formula was obtained that describes the total probability of single-photon absorption of an USP (during all time of its action) in terms of the spectral cross-section of photoabsorption and the Fourier transform of the strength of the electric field in a pulse. The expression derived in the work [12] was widely used further for analysis of single-photon absorption and spontaneous scattering by various targets [13][14][15].The present work is dedicated to the theoretical analysis of two-photon excitation of atoms in a discrete energy spectrum by ultrashort electromagnetic pulses of femto-and