Chaos and nonlinearities in high harmonic generation

Linearity is a fundamental postulate of quantum mechanics which is occasionally the subject of debate. This paper investigates the possibility of checking this assumption by using a laser field. We study the corrections caused by the presence of a small nonlinearity in the Hamiltonian of a quantum system. As a model we use a simplified two-level quantum system whose states are coupled by a small off-diagonal term proportional to the population of the upper level. The nonlinearity causes spontaneous decay of the upper level, shift and broadening of the line and the sensitive dependence of the final state on the initial condition. The presence of a strong laser field, resonant with the atomic transition, enhances the population transfer among the levels and introduces quantitative and qualitative modifications of the spectra of high order harmonic generation (HHG); these are cumulative effects which can be subject to experimental checks. Experiments are needed in order to set an upper limit to the nonlinear term.