We study the homogenization of a Schrödinger equation
in a periodic medium with a time dependent potential.
This is a model for semiconductors excited by an external
electromagnetic wave. We prove that, for a suitable choice
of oscillating (both in time and space) potential, one can
partially transfer electrons from one Bloch band to another.
This justifies the famous "Fermi golden rule" for the transition
probability between two such states which is at the basis
of various optical properties of semiconductors.
Our method is based on a combination of classical homogenization
techniques (two-scale convergence and suitable oscillating test
functions) and of Bloch waves theory.