Generation and Propagation of Coherent Matter Waves

Bose-Einstein condensates (BECs) realized with dilute alkali atoms can be considered as a source of coherent matter waves, what is sometimes termed atom laser. We will review the experimental methods used to create and manipulate BECs. We will also illustrate some simple atom-optical elements that can be created. We will review the propagation of coherent matter waves in periodic potentials showing how it is possible to control matter wave dispersion and create gap solitons.