Ultracold atoms in optical lattice

In this thesis, a Bose-Einstein condensate is loaded into a three-dimensional optical lattice potential formed by a standing wave laser light field. Ultracold bosons trapped harmonic plus optical potential is studied. The band structure together with Bloch functions and Wannier basis are discussed for this system. Using tight-binding method, corresponding discrete equation and investigate quantum dynamics for a modulated optical potential is derived. Analytical solution and perform numerical computation are found. Dynamical localization in our system is reported.