  We develop a non-equilibrium many-body theory of the coherent femtosecond
nonlinear optical response of the Fermi edge singularity. We study the role of
the dynamical Fermi sea response in the time-evolution of the pump-probe
spectra. The electron-hole correlations are treated nonperturbatively with the
time-dependent coupled cluster cxpansion combined with the effective
Hamiltonian approach. For short pulse durations, we find a non-exponential
decay of the differential transmission during negative time delays, which is
governed by the interactions. This is in contrast to the results obtained
within the Hartree-Fock approximation, which predicts an exponential decay
governed by the dephasing time. We discuss the role of the optically-induced
dephasing effects in the coherent regime.
