Fermionic superfluidity in confined one-dimensional spin-imbalanced systems: A configuration-space Hartree-Fock-Bogoliubov approach

We study pairing and density correlations in imbalanced one-dimensional Fermi systems with short-range interactions that are spatially confined by either a harmonic or a hard-wall (or "box") trapping potential. It has been hoped that such systems, which can be realized using ultracold atomic gases, would exhibit the long-sought-after Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our approach applies a general Hartree-Fock-Bogoliubov (HFB) transformation to handle spatially-inhomogeneous pairing and density correlations on an equal footing to yield predictions for the ground state of confined 1D Fermi gases in harmonic and hard-wall traps. We find that while both cases yield a spatially modulated FFLO pairing amplitude in the imbalanced regime, in the case of a harmonic trap the corresponding signature in the local density is rather weak. In contrast, in the hard-wall case, we find a strong reflection of the FFLO pairing in the local in situ densities. In particular, we find that the excess spins are strongly localized near nodes in the pairing amplitude, thus creating an unmistakable signature of the FFLO state in a hard-wall box trap.