Ultracold atoms in optical lattices: tunable quantum many-body systems

Abstract

Cold atoms in optical lattices offer an exciting new laboratory where quantum many-body phenomena can be realized in a highly controlled way. They can even serve as quantum simulators for notoriously difficult problems like high-temperature superconductivity. This review is focussed on the recent developments and new results in multi-component systems. Fermionic atoms with SU(N) symmetry have exotic superfluid and flavor-ordered ground states. We discuss symmetry breaking, collective modes, and detection issues, e.g. in Bragg scattering. On the other hand, bosonic multiflavor ensembles allow for engineering of spin Hamiltonians which are interesting from a quantum computation point of view. Finally, we address the role of disorder in optical lattices. Fermionic atoms experience Anderson localization at sufficiently strong disorder. Interactions among the atoms induce a competing tendency towards delocalization. We present a complete phase diagram obtained within dynamical mean-field theory and discuss experimental observability of the Mott and Anderson phases.

Acknowledgements

The author would like to thank E. Altman, B. Byczuk, I. Cirac, E. Demler, C. Honerkamp, M.D. Lukin, D. Vollhardt, and P. Zoller for collaborations, and M. Zwierlein and W. Ketterle for discussions on this topic.