"In this project we will experimentally study the behaviour of light and matter on the timescales, at which their fundamental properties are being formed. We define such critical timescales as:For light - the timescale of a single optical cycle. This naturally requires the sub-cycle time resolution in the experiments.For matter – the time during which the quantum-mechanical dimensionality (e.g. 0D or 3D) in the material can be established or significantly modified.We want to find out how fast do some of the fundamental physical phenomena occur, and what exactly governs these critical timescales. Presently there is no concrete answer to this “how fast?” question regarding establishment of many physical properties. Many phenomena are simply referred to as “instantaneous”, i.e. occurring on zero timescale, which is a euphemism for “we don’t know how fast they are”.Using nonlinear ultrafast terahertz (THz) spectroscopy as an experimental method, and semiconductors as a material system, in this project we will investigate the following problems:1) Development of optical supercontinuum from a single cycle of light in a nonlinear medium. We aim to directly observe the synthesis of new frequencies in the optical signal.2) How fast can one modulate a simple quantum-mechanical system by an external field? How fast is Stark effect, and what constitutes the maximum electro-absorption modulation speed limit?3) How fast is the creation of quantum-mechanical dimensionality in a crystal? How fast the energy band in a crystal, a result of interference of the wavefunctions of individual atomic potentials, is formed? What governs this time scale? Is it the reciprocal of energy width of the band?"