Confinement versus deconfinement of Cooper pairs in one-dimensional spin-3/2 fermionic cold atoms

The 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. Finally, we reveal the existence of a bond-ordered Mott insulating phase in some part of the repulsive regime.