  We study theoretically the ultrafast nonlinear optical response of quantum
well excitons in a perpendicular magnetic field. We address the role of
many-body correlations originating from the electron scattering between Landau
levels (LL). In the linear optical response, the processes involving inter-LL
transitions are suppressed provided that the magnetic field is sufficiently
strong. However, in the nonlinear response, the Auger processes involving
inter-LL scattering of two photoexcited electrons remain unsuppressed. We show
that Auger scattering plays the dominant role in the coherent exciton dynamics
in strong magnetic field. We perform numerical calculations for the third-order
four-wave-mixing (FWM) polarization which incorporate the Auger processes
nonperturbatively. We find that inter-LL scattering leads to a strong
enhancement and to oscillations of the FWM signal at negative time delays.
These oscillations represent quantum beats between optically-inactive
two-exciton states related to each other via Auger processes.
