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Motivated by the realization of hard-wall boundary conditions in experimentswith ultracold atoms, we investigate the ground-state properties of spin-1/2fermions with attractive interactions in a one-dimensional box. We use latticeMonte Carlo methods to determine essential quantities like the energy, which wecompute as a function of coupling strength and particle number in the regimefrom few to many particles. Many-fermion systems bound by hard walls displaynon-trivial density profiles characterized by so-called Friedel oscillations(which are similar to those observed in harmonic traps). In non-interactingsystems, the characteristic length scale of the oscillations is set by (2kF)^(-1), where kF is the Fermi momentum, while repulsive interactions tend togenerate Wigner-crystal oscillations of period (4 kF)^(-1). Based on thenon-interacting result, we find a remarkably simple parametrization of thedensity profiles of the attractively interacting case, which we generalize tothe one-body density matrix. While the total momentum is not a conservedquantity in the presence of hard walls, the magnitude of the momentum doesprovide a good quantum number. We are therefore able to provide a detailedcharacterization of the (quasi-)momentum distribution, which displays ratherrobust discontinuity at the Fermi surface. In addition, we determine thespatially varying on-site density-density correlation, which in turn yieldsTan's contact density and, upon integration, Tan's contact. As is well known,the latter fully determines the short-range correlations and plays a crucialrole in a multitude of equilibrium and non-equilibrium sum rules.

journal of physics. b, atomic molecular and optical physics/journal of physics. b, atomic, molecular and optical physics

Ground-state energy, density profiles, and momentum distribution of  attractively interacting 1D Fermi gases with hard-wall boundaries: a Monte  Carlo study