It is shown that the ultrafast coherent nonlinear optical effect of in
teraction-induced polarization rotation can be used to identify and st
udy interaction processes in many-body systems. In the theoretical exa
mple presented here, signatures of coherent exciton-exciton interactio
ns are identified in polarization trajectories in Poincare's Cartesian
complex plane of polarization, which is used to visualize the differe
ntial polarization rotation (or, alternatively, the polarization of th
o reflected light) of femtosecond light pulses in uniaxially strained
quantum wells. Interaction processes are found to affect significantly
the polarization trajectories, including their symmetry properties.