Optical coupling and parametric sideband generation in a semiconductor bound exciton

Group theoretical techniques are used to deduce the selection rules and energy splitting of the electric dipole absorption lines $\Gamma_6\rightarrow\Gamma_8$, $\Gamma_7 \rightarrow\Gamma_8$ of a donor exciton in a tetrahedral semiconductor, e.g., GaAs. We obtain selection rules for the above transitions for the spin states $\Delta m_j$. The application in a bound exciton system in a magnetic field for the purposes of obtaining electromagnetically induced transparency is discussed. In particular, Stokes and Anti Stokes couplings have been experimentally observed in such a system. We theoretically calculate the expected gains of the Stokes and anti Stokes couplings for $\sigma$- and $\pi$- polarization of the pump field. We show that the system can be interpreted as one exhibiting double $\Lambda$-type transitions, and therefore could be used for coherent non-linear optics and, ultimately, quantum-optics based quantum information processing.