Abstract
The combined effect of an artificial magnetic field and particle interactions is an extremely vast subject, giving rise to numerous phenomena in Quantum Condensed Matter Physics: ferro- and antiferromagnetism, the quantum Hall effect, superconductivity and the Meissner effect, spintronics, insulators and topological superconductors, etc. We have tackled this type of problem by focusing on the behavior of a superfluid in the presence of a uniform magnetic field. We have tackled this type of problem by focusing on the behavior of a superfluid in the presence of a uniform magnetic field. We considered a condensate of repulsively interacting bosons placed in a rotating harmonic trap. This apparently very simple system has enabled us to introduce a series of important notions: the mean-field approximation, the critical frequency for vortex nucleation, Abrikosov lattices, and finally the transition to strongly correlated states, one of the great challenges currently open in cold atom physics.
