  We provide analytic solutions of the optical Bloch equations for a two-level
system interacting with a broadband light field. We will focus on two special
examples: incident light with a Lorentzian spectral density and the limit of
incident monochromatic light. The results are used to obtain an expression for
the nonlinear polarizability of a two-level atom irradiated by a wave with a
Lorentzian spectral density.
