Ultrafast coherent spectroscopy of single semiconductor quantum dots

Excitonic and spin excitations of single semiconductor quantum dots currently attract attention as possible candidates for solid state based implementations of quantum logic devices. Due to their rather short decoherence times in the picosecond to nanosecond range, such implementations rely on using ultrafast optical pulses to probe and control coherent polarizations. In this article, we review our recent work on combining ultrafast spectroscopy and near-field microscopy to probe the nonlinear optical response of a single quantum dot and of a pair of dipolecoupled quantum dots on a femtosecond time scale. We demonstrate coherent control of both amplitude and phase of the coherent quantum dot polarization by studying Rabi oscillations and the optical Stark effect in an individual dot. By probing Rabi oscillations in a pair of dots, we identify couplings between permanent excitonic dipole moments. Our results show that although semiconductor quantum dots resemble in many respects atomic systems, Coulomb many-body interactions can contribute significantly to their optical nonlinearities on ultrashort time scales. This paves the way towards the realization of potentially scalable nonlocal quantum gates in chains of dipole-coupled dots, but also means that decoherence phenomena induced by many-body interactions need to be carefully controlled.