Quantum atomic gases cooled down to the nK scale represent a combined theoretical and experimental platform, where extreme quantum degeneracy conditions can be realized after tuning a number of knobs: temperature, interactions strength and range, dimensionality, disorder level, while trapping the atoms in different geometries and in the presence of gauge fields. In fact, due to highly controllable experimental conditions and theoretical modelling, current cross-disciplinary efforts are focused towards implementing the seminal Feynman idea of a quantum simulator: in essence, coding in a controllable (quantum) system the analog simulation of the (quantum) system under study.
In this talk, after reviewing the toolbox available in the experimental platform, I will discuss this general idea via selected different theoretical problems along with their corresponding experimental realization: the BCS-BEC crossover, the Luttinger-liquid behavior of 1D dipolar Bose gases, the incommensurate phases of bosonic ladders in artificial gauge fields, quantum effects in the Aubry transition, and many-fermions entanglement as a new paradigm for metrology applications.