  The nonlinear optical response of a system of molecules often contains
contributions whereby the products of lower-order processes in two separate
molecules give signals that appear on top of a genuine direct higher-order
process with a single molecule. These many-body contributions are known as
cascading and complicate the interpretation of multidimensional stimulated
Raman and other nonlinear signals. In a quantum electrodynamic (QED) treatment,
these cascading processes arise from second-order expansion in the molecular
coupling to vacuum modes of the radiation field, i.e., single-photon exchange
between molecules, which also gives rise to other collective effects. We
predict the relative phase of the direct and cascading nonlinear signals and
its dependence on the microscopic dynamics as well as the sample geometry. This
phase may be used to identify experimental conditions for distinguishing the
direct and cascading signals by their phase. Higher-order cascading processes
involving the exchange of several photons between more than two molecules are
discussed as well.
