We give a detailed description of a novel method for time-resolved
experiments on single non-luminescent nanoparticles. The method is based on the
combination of pump-probe spectroscopy and a common-path interferometer. In our
interferometer, probe and reference arms are separated in time and polarization
by a birefringent crystal. The interferometer, fully described by an analytical
model, allows us to separately detect the real and imaginary contributions to
the signal. We demonstrate the possibilities of the setup by time-resolved
detection of single gold nanoparticles as small as 10 nm in diameter, and of
acoustic oscillations of particles larger than 40 nm in diameter