Phase averaging for calculations involving two-color intense-field excitation

Abstract

A general and computationally efficient method for averaging both the time-dependent and the steady-state atomic or molecular state populations over the phases, ${\ensuremath{\delta}}_{1}$ and ${\ensuremath{\delta}}_{2},$ of two continuous-wave laser fields involved in an excitation process is developed based on the Floquet formalism. Explicit calculations are presented for the coherent one- and three-photon electronic excitation of a two-level model molecule in order to illustrate the importance of phase averaging in situations where the relative phase difference between the two fields is fixed. While the explicit results involve electronic excitation, they are presented in reduced form so that they can be scaled to other regions of the electromagnetic spectrum and to other field strengths. The results have important implications in situations where the relative phase difference between two intense continuous-wave laser fields is used to control the excitation process.