  While time-resolved pump-probe differential reflectivity and transmitivity
measurements are routinely used to monitor the population relaxation dynamics
on the subpicosecond time scale, it is also known that the signal in the
negative delay can yield direct signatures of the
perturbed-free-induction-decay of polarization. Yet this technique, especially
in reflection geometry, has never been popular because the experiment is
conceptually not very intuitive. Coherent dynamics is therefore usually studied
using the more complex four-wave-mixing experiments. Here we derive from first
principles the simplest possible but mathematically complete framework for the
negative delay signal in both the time and the spectral domains. The
calculation involving the optical Bloch equations to describe the induced
polarization and the Ewald-Oseen idea to calculate the reflected signal as a
consequence of the free oscillations of perturbed dipoles, also explicitly
includes the process of lock-in detection of a double-chopped signal after it
has passed through a monochromator. The theory is compared with experiments on
high quality GaAs quantum well sample. The dephasing time inferred
experimentally at 4 K compares remarkably well with the inverse of the
absorption linewidth of the continuous-wave photoluminescence excitation
spectrum. Spectrally resolved signal at negative delay calculated from our
theoretical expression nicely reproduces the coherent spectral oscillations,
although exact fitting of the experimental spectra with the theoretical
expression is difficult. This is on account of additional resonances present in
the sample corresponding to lower energy bound states.
