Strong correlation effects and quantum information theory of low dimensional atomic gases

These lecture notes present an introduction to the strongly correlated regime of low dimensional atomic gases. The discussion is concentrated on situations in which the strongly correlated limit is achieved by creating degeneracies in the one-particle motional states. Three different schemes of experimental relevance are analyzed: bosonic atoms in a two dimensional rapidly rotating trap, bosonic atoms in a one dimensional optical lattice, and bosonic atoms with frozen motional degrees of freedom and two internal states. The cot-responding entangled multiparticle states (Laughlin liquids, Mott phases, squeezed states), and the different strongly correlated phenomena that appear (fermionization, fractional statistics) are studied. Emphasis is given to the possibility of observing novel strongly correlated phenomena as well as to the possible implementations for quantum computation and quantum information.