We review basic quantum electrodynamics and quantum optics aspects in microstructures that exhibit a gap in the spectrum of the electromagnetic radiation they support, known as photonic crystals. After a brief sketch of the properties of such materials we discuss the behaviour of few-level atoms or collections thereof with transition frequencies inside and in the vicinity of the gap. The discussion is cast in terms of a unified formalism which facilitates the comparison with standard cavity-atom physics.

We study the dynamics of single-electron transport in a linear array of tunnelcoupled quantum dots. We show that this system can serve as an ideal quantum channel, enabling a controlled transport and entanglement of electrons in a large-scale integrated quantum computer.

We present a detailed theoretical analysis of superradiant Rayleigh scattering from atomic Bose-Einstein condensates. A thorough investigation of the spatially resolved time-evolution of optical and matter-wave fields is performed in the framework of the semiclassical Maxwell-Schrödinger equations. Our theory is not only able to explain many of the known experimental observations, e.g., the behavior of the atomic side-mode distributions, but also provides further detailed insights into the coupled dynamics of optical and matter-wave fields. To work out the significance of propagation effects, we compare our results to other theoretical models in which these effects are neglected.