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We show that it is possible to use a piecewise constant Hamiltonian to describe the main features of the dynamics of an atom interacting with a laser field. In particular we show that using this approximation we are able to give a good description of the ionization signal, of the HHG spectra and of the attosecond pulses generated by the radiating electron. Finally, we give an explicit formula to evaluate the ionization rate in the time dependent laser field. This formula, which is a generalization of the Landau formula for the ionization rate of an atom in a static electric field, fairly well reproduces the numerical ionization rates for a broad range of laser frequency and intensity. The main advantage of this formula is that it can be used well beyond the limits of the quasi-static formula for the ionization rate of an atom.

A new scheme to generate isolated attosecond pulses is presented that involves the use of a laser field and of a unipolar field. The laser field has a pulse of intensity I = 1.5×1014 W cm−2 and wavelength λ = 820 nm. The unipolar pulse is an asymmetric pulse consisting of a sharp peak, lasting approximately half a laser period, i.e. nearly 1.4 fs, followed by a long and shallow tail. We show that on combining these two fields, it is possible to generate isolated attosecond pulses as short as 1/10 of a laser period, i.e. approximately 270 as. Moreover, it is argued that this scheme is robust either against small variations of the laser envelope, or against small changes in the delay between the laser pump and the unipolar pulse.