The pure dephasing of the optical polarization and the corresponding line shape of absorption spectra in small quantum dots due to the interaction of the exciton both with optical and acoustic phonons is calculated. By restricting ourselves to the exciton ground state we obtain a model which is known to be exactly solvable. We study the temperature dependence and the influence of a static electric field. The spectra exhibit strongly non-Lorentzian line shapes including a sharp zero-phonon line. Optical phonons lead to phonon sidebands which may acquire a finite width due to the dispersion of the phonon branch; the width increases with decreasing dot size. Acoustic phonons both due to deformation potential and piezoelectric coupling lead to a broad background in the spectra which is strongly temperature dependent. Typical features of the spectra are qualitatively well reproduced by a perturbative approach based on one-phonon processes. Multiphonon processes, however, give significant contributions in particular in the case of acoustic phonons. Lateral or vertical electric fields lead to an increasing efficiency of the polar interaction mechanisms while deformation potential interaction is much less influenced.

The authors review the physics of ultrafast dynamics in semiconductors and their heterostructures, including both the observed experimental phenomena and the theoretical description of the processes. These are probed by ultrafast optical excitation, generating nonequilibrium states that can be monitored by time-resolved spectroscopy. Light pulses create coherent superpositions of states, and the dynamics of the associated phase relationships can be directly investigated by means of many-pulse experiments. The commonly used experimental techniques are briefly reviewed. A variety of different phenomena can be described within a common theoretical framework based on the density-matrix formalism. The important interactions of the carriers included in the theoretical description are the phonon interactions, the interactions with classical and quantum light fields, and the Coulomb interaction among the carriers themselves. These interactions give rise to a strong interplay between phase coherence and relaxation, which strongly affects the nonequilibrium dynamics. Based on the general theory, the authors review the physical phenomena in various semiconductor structures including superlattices, quantum wells, quantum wires, and bulk media. Particular results which have played a central role in understanding the microscopic origins of the relaxation processes are discussed in detail.

We report on Rabi oscillations of the biexciton in a single ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dot, induced via a coherent two-photon process. In contrast to single-exciton Rabi oscillations the measured population oscillation is not purely sinusoidal in excitation pulse area. The experimental results are well reproduced by a theoretical calculation that relies only on the pulse shape and biexciton binding energy. Dephasing times of the biexciton are similar to those of the single exciton under the applied measurement conditions reaching up to $220\mathrm{ps}$.