The phenomena of quantum coherence has been applied with great success in the atomic systems. For optoelectronic applications the interest is inherently directed towards the semiconductor heterostructures. Large number of works have proposed and analyzed the atomic quantum coherence effects in the semiconductors. In this respect, nanocrystals (NCs) are very promising structures for seeking the quantum coherence phenomena due to their atomic-like electronic structure. Furthermore, their robust structure, integrability and larger excitonic lifetimes with respect to atomic systems makes them more promising candidates for the technological applications. Within an atomistic pseudopotential electronic structure framework, the optical Bloch equations (OBEs) originating from atomic coherence theory are derived and solved numerically for Ge NCs. The results are interpreted in the context of coherent population oscillations (CPO). Narrow dips are observed in the absorption profiles which corresponds to high dispersions within a transparency window and produce slow light. A systematic study of the size-scaling of slow-down factor with respect to NC diameter and controllable slow light by applying external Stark field are provided. The results indicate that Ge NCs can be used to generate optically and electrically controllable slow light. The many-body Coulomb interactions which underlie the quantum coherence and dephasing are of central importance in semiconductor quantum confined systems. The effects of many-body interactions on the optical response of Ge NCs have been analyzed. The semiconductor optical Bloch equations (SBEs) are derived in a semiclassical approach and the Coulomb correlations are included at the level of Hartree-Fock approximation.