Playing with Atoms in Optical Lattices: a Lego for Condensed-Matter Theoreticians

The new found ability to confine ultracold quantum atomic gases in optical lattices is already having a great impact in fields as diverse as condensed matter physics and quantum information processing. These artificial crystals of light offer a unique level of control over almost all parameters: the periodic structure, the atomic interactions, the internal degrees of freedom, etc. This allows us to explore a whole range of fundamental quantum phenomena which are extremely difficult (or almost impossible) to study in real materials. Moreover, it makes real the ambitious dream of engineering novel many-body quantum phases. In my talk, I will first give an overview of how this field has been born and developed in the last three years. I will then illustrate the possibilities of atoms in optical lattices
with two parts of my recent work. First, I will report on the
creation for the first time of the so called Tonks-Girardeau gas,
a novel state of matter in which bosons, that usually like to be
together in the same quantum state, behave, however, as picky
lonely fermions. Then, I will show how to use atoms in optical
lattices to simulate quantum random systems in parallel, that is,
with all possible quantum paths of the random system taking place
at the same time. This proposal, which uses the optical lattice as
a kind of quantum computer, may pave the way of a better
understanding of disorder in quantum many-body systems.