Hofstadter “butterfly”: Spectrum of a single particle moving in non-abelian SU(2) gauge field generated by the lasers, as a function of the two “magnetic” fluxes

Quantum gauge theories and ultracold atoms

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Ultracold gases in optical lattices can simulate dynamics of matter field in artificial external non-abelian gauge fields, and of (abelian) gauge fields. The relevance of the latter ranges from relativistic systems, like Dirac fermions or topological insulators, to strongly correlated systems (fractional quantum Hall states). We have recently proposed how to realize such simulators experimentally. The design of feasible proposals for dynamical gauge fields paves the way to ``cold atoms'' solutions of long standing problems in high energy/condensed matter physics as confinement and high temperature superconductivity.

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