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We study spin 3/2 fermionic cold atoms with attractive interactions confinedin a one-dimensional optical lattice. Using numerical techniques, we determinethe phase diagram for a generic density. For the chosen parameters,one-particle excitations are gapped and the phase diagram is separated into tworegions: one where the two-particle excitation gap is zero, and one where it isfinite. In the first region, the two-body pairing fluctuations (BCS) competewith the density ones. In the other one, a molecular superfluid (MS) phase, inwhich bound-states of four particles form, competes with the densityfluctuations. The properties of the transition line between these two regionsis studied through the behavior of the entanglement entropy. The physicalfeatures of the various phases, comprising leading correlations, Friedeloscillations, and excitation spectra, are presented. To make the connectionwith experiments, the effect of a harmonic trap is taken into account. Inparticular, we emphasize the conditions under which the appealing MS phase canbe realized, and how the phases could be probed by using the density profilesand the associated structure factor. Lastly, the consequences on the fluxquantization of the different nature of the pairing in the BCS and MS phasesare studied in a situation where the condensate is in a ring geometry.

the european physical journal. b, condensed matter physics/european physical journal. b, condensed matter and complex systems

Spin 3/2 fermions with attractive interactions in a one-dimensional  optical lattice: phase diagrams, entanglement entropy, and the effect of the  trap