Collective Excitations and the Dynamical Stark Effect in a Coherently Driven Exciton System

We consider a semiconductor of arbitrary dimension subject to a strong monochromatic laser beam in the transparency region below the exciton resonance. We calculate the spectrum of collective excitations and explain the recently observed dynamical Stark effect of the exciton. For the first time, we derive from first principles the nonresonant nonlinear susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ including exciton correlations.