Strongly Interacting Quantum Mixtures of Ultracold Atoms

In what forms does matter organize itself under the influence of interaction? This is the fundamental question of many-body physics, which arises at all length scales: from the dense quark matter present in the beginning of our Universe, to the atomic nucleus, the electrons inside a metal, and the inner workings of a neutron star. However, strong interactions between particles do not allow for a simple description of such systems. Strongly interacting mixtures of ultracold atoms will allow us to realize complex many-body systems relevant to the description of High-T$_C$ and Giant Magnetoresistance materials and which cannot be simulated theoretically. We are constructing a new apparatus that will allow to cool three different species of atoms, two of them fermionic, $^6$Li and $^{40}$K, and one of them bosonic, $^{23}$Na. A two-species Fermi-Fermi mixture close to a Feshbach resonance realizes an unusual form of fermionic superfluid with unequal masses. A mass- and number imbalanced Fermi mixture might give access to new states of fermionic matter, such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase of Cooper pairs with non-zero momentum.