From strongly interacting atomic systems to optical lattices

For more than a decade, cold atoms represented weakly interacting systems. Laser cooling achieved temperatures typically around 100 μK in a classical gas, far away from quantum degeneracy. Evaporative cooling led to Bose-Einstein condensation at temperatures typically around 100 nK. Bose-Einstein condensates are weakly interacting many-body systems described by mean field physics through the Gross-Pitaevskii equation. The next milestone was the cooling of fermions to quantum degeneracy. Strong interactions led to pairing and fermionic superfluidity. The exploration of the BEC-BCS crossover was a major achievement. These systems show strong pair correlations, but the pairs can still be described by a mean field approximation. Correlations become stronger when the kinetic energy is small compared to the interaction energy. Strongly correlated matter has been created in optical lattices which reduces the kinetic energy, and trough Feshbach resonances which enhance the interaction energy. Strong correlations in optical lattices lead to Mott insulator physics.