Confinement versus deconfinement of Cooper Pairs in One-Dimensional Spin-3/2 Fermionic Cold Atoms

4 pages, 7 figuresInternational audienceThe phase diagram of spin-3/2 fermionic cold atoms trapped in a one-dimensional optical lattice is investigated at quarter filling (one atom per site) by means of large-scale numerical simulations. In full agreement with a recent low-energy approach, we find two phases with confined and deconfined Cooper pairs separated by an Ising quantum phase transition. The leading instability in the confined phase is an atomic-density wave with subdominant quartet superfluid instability made of four fermions. At sufficiently low densities, we find that the quartet instability dominates and marks the onset of a nematic Luttinger liquid phase associated to the pairing of Cooper pairs