Ultracold quantum gases in optical lattices

Ultracold bosonic and fermionic quantum gases are versatile and robust systems for probing fundamental condensed-matter physics problems1–12, as well as fi nding applications in quantum optics and quantum information processing13 and understanding atomic and molecular physics14,15. Storing such ultracold quantum gases in artifi cial periodic potentials of light has opened innovative manipulation and control possibilities, in many cases creating structures far beyond those currently achievable in typical condensed-matter physics systems. Amazingly, strong correlation eff ects can be observed in dilute atomic gases despite the densities of the particles in the trapping potentials being more than fi ve orders of magnitude less than that of the air surrounding us! Ultracold quantum gases in optical lattices can in fact be considered as quantum simulators, as Richard P. Feynman originally conceived for a quantum computer: a powerful simulator in which a highly controllable quantum system can be used to simulate the dynamical behaviour of another complex quantum system16,17. As a simulator, an optical lattice off ers remarkably clean access to a particular hamiltonian and thereby serves as a model system for testing fundamental theoretical concepts, at times providing textbook examples of quantum many-body eff ects.