  We study theoretically the coherent nonlinear optical response of doped
semiconductors with partially occupied subbands. When the Fermi energy of an
occupied subband approaches the exciton level of an upper subband, the
absorption spectrum acquires a characteristic double-peak shape originating
from the interference between the Fermi-edge singularity and the exciton
resonance. We demonstrate that, for the off-resonant pump excitation, the
pump/probe spectrum undergoes a dramatic transformation in the coherent regime,
with a strong time-dependent exchange of oscillator strength between Fermi edge
singularity and exciton peaks. We show that this effect originates from the
many-body electron-hole correlations which determine the dynamical response of
the Fermi see. To calculate the nonlinear absorption spectrum, we use the
coupled cluster method combined with time-dependent Schrieffer-Wolff
transformation. Possible experimental applications are discussed.
