Line shapes and photon echoes within a generalized Kubo model

Kubo introduced a stochastic model of frequency fluctuations that naturally leads to an understanding of homogeneous and inhomogeneous broadening in condensed phase spectroscopy. In this Letter we discuss a generalized Kubo model that has two different timescales. The model is relevant for a variety of different physical situations, and in certain limits describes combined homogeneous and inhomogeneous broadening. We explore the limits of applicability of this homogeneous/inhomogeneous phenomenology for both the line shape and the integrated two-pulse photon echo intensity. Our results have implications for non-linear ultrafast liquid-state spectroscopy.