Analytic Expressions for a Spin-Half Particle Dressed by a Polychromatic Field.

Analytic expressions are derived for the time evolution of a spin half in a multi-frequency coherent field, described by a polychromatic Rabi model. We transform to a picture where the spin is dressed progressively by each frequency component of the field. In this picture the time evolution operator takes a simple approximate form, and can be transformed back to the undressed picture where it contains resonant and off-resonant terms. Furthermore, we simplify these transformations to leading order in the field amplitudes, and describe the some of the dominant effects in such multi-frequency processes.