  Although semiconductor Bloch equations have been widely used for decades to
address ultrafast optical phenomena in semiconductors, they have a few
important drawbacks: (i) Coulomb terms between free electron-hole pairs require
Hartree-Fock treatment which, in its usual form, preserves excitonic poles but
loses biexcitonic resonances. (ii) Solving the resulting coupled differential
equations imposes heavy numerics which completely hide the physics. This can be
completely avoided if, instead of free electron-hole pairs, we use correlated
pairs, i.e., excitons. Their interactions are easy to handle through the
recently constructed composite-exciton many-body theory, which allows us to
\emph{analytically} obtain the time evolution of the polarization induced by a
laser pulse. This polarization comes from Coulomb interactions between virtual
excitons, but also from Coulomb-free fermion exchanges, which are dominant at
large detuning.
