  Phase-modulated non-linear spectroscopy with higher harmonic demodulation has
recently been suggested to provide information on many-body excitations. In the
present work we theoretically investigate the application of this method to
infer the interaction strength between two particles that interact via weak
dipole-dipole interaction. To this end we use full numerical solution of the
Schr\"odinger equation with time-dependent pulses. For interpretation purpose
we also derive analytical expressions in perturbation theory. We find one can
detect dipole-dipole interaction via peak intensities (in contrast to
line-shifts which typically are used in conventional spectroscopy). We provide
a detailed study on the dependence of these intensities on the parameters of
the laser pulse and the dipole-dipole interaction strength. Interestingly, we
find that there is a phase between the first and second harmonic demodulated
signal, whose value depends on the sign of the dipole-dipole interaction.
