**Coherent Optical Control and Related Phenomena**

Quantum coherent control represents a universal approach for predictable manipulation of the properties of the quantum systems, such as atoms and molecules, most recently applied to solid state systems. Coherent-optical control in semiconductor nanostructures has recently attracted significant interest because it allows coherent manipulation of the carrier wave functions on a time scale shorter than typical dephasing times. This in turn is a prerequisite for successful implementation of ultrafast optical switching and quantum-information processing. A necessary condition for quantum coherence is the use of sufficiently short optical pulses so that they can interact with the quantum system before it can be affected by its environment.

We have developed a general dynamical model for description of the coherent interactions of ultrashort linearly- and circularly-polarised optical pulses with the resonant nonlinearities in planar optical waveguides and semiconductor microcavities in multi-dimensions. The adopted approach models the coherent light-matter interaction exploiting SU(N) Lie group symmetries in a discrete multi-level quantum system and the full vectorial treatment of the electromagnetic wave propagation. For the case of a generic N-level system this approach is based on the expansion of the density matrix and the system Hamiltonian in terms of the SU(N) Lie algebra generators. The time-evolution of the quantum system in the external dipole-coupling perturbation is described in terms of a real pseudospin vector representation coupled to the vectorial Maxwellâ€™s equations for the optical field propagation. The latter permits a rigorous description of pulse propagation and interactions on an ultrashort time scale