Today electronic and optoelectronic devices use roughly 1 billion of electrons or photons. They rely thus on the laws of statistical physics with irreversibility and energy dissipation as prevailing factors. The next generation – so called quantum devices – will overcome these limitations by using single charges or photons. Their dynamics is governed by the unitary quantum evolution which is probabilistic but reversible. Therefore development and to demonstration of novel concepts for the quantum control of charge and spin excitations as well as their coupling with photons in artificially grown solid-state nanostructures is of great interest. A major problem in solid-state is decoherence that destroys the unitary quantum evolution. For this reason, special emphasis is concentrated on semiconductor quantum dots (QDs) where the excitations are largely decoupled from the environment. Highly advanced growth techniques such as molecular beam epitaxy allow indeed to fabricate QD heterostructures that exhibit properties similar to artificial atoms.However, owing to the specific features of a semiconductor like the band structure and crystal field, the interaction with phonons and external magnetic fields as well as the radiative coupling, fundamentally new physics arise. In combination with their extremely small size enabling an enormous degree of integration up to 1011 per cm2 and the potential of high speed optical switching on the fs-timescale, QDs are very promising candidates for the building blocks in quantum information processing.
However, in order to achieve these goals, it is crucial, first, to elucidate the decoherence mechanisms in QDs and, second, to uncover principles that allow for the manipulation of their charge and spin states. Due to the flexible time structure of light, optical techniques are of particular interest. In this context, one has also to develop concepts how the coupling between photons and individual QDs can be contro- led. In this tutorial an overview of coherent optical phenomena in semiconductor QDs is presented. Ultrafast optical spectroscopy provides essential information on dynamical properties of charge and spin states in condensed matter. This includes quantum mechanical evolution of optically prepared electronic states, their decoherence and relaxation processes. Optical techniques such as ultrafast pump probe, transient four-wave mixing in combination with magnetic field and polarization sensitive excitation and detection represent a powerful set of methods. Various coherent phenomena such as Rabi oscillations, Ramsey fringes and free induction decay were demonstrated for electron-hole (exciton) excitations which can be often considered as a three level V-type scheme . In its turn, QDs with excess carriers, e.g. electrons, represent a different system where the ground state is a doublet with spin eigenstates +1/2 and −1/2. Interaction with light can be considered as two coupled Λ schemes with long-lived coherence in the ground state . Here demonstration of coherent spin control is accomplished via direct coherent excitation or detuned optical pulses via optical Stark effect [3–6]. In the final part I will also discuss the current state of the art in coherent spectroscopy based on two- and three- dimensional Fourier spectroscopy allowing to get comprehensive information about the energy structure and coherent interactions between different types of excitations in QDs [7,8].