Simple formula for photoprocesses in ultrashort electromagnetic field

Within the framework of the perturbation theory, a simple formula for the probability of a photoprocess for the whole time of action of an ultrashort electromagnetic pulse has been derived, when the concept of spectral intensity of radiation and probability per unit time is inapplicable. In the obtained formula the total probability is expressed in terms of the cross-section of a photoprocess in a monochromatic field and the Fourier transform of electric field strength. The advanced approach is applied for the analysis of photoabsorption of an atom and a metal nanosphere under the action of a subcycle laser pulse with a changeable value of the carrier–envelope phase. The expressions for probability and energy of photoabsorption in the limit of a zero pulse duration have been obtained.