Correlations of the Upper Branch of 1D Harmonically Trapped Two-Component Fermi Gases

Abstract

We present highly accurate energy spectra and eigenfunctions of small 1D harmonically trapped two-component Fermi gases with interspecies δ-function interactions, and analyze the correlations of the so-called upper branch (i.e., the branch that describes a repulsive Fermi gas consisting of atoms but no molecules) for positive and negative coupling constants. Changes of the two-body correlations as a function of the interspecies coupling strength reflect the competition of the interspecies interaction and the effective repulsion due to the Pauli exclusion principle, and are interpreted as a few-body analog of a transition from a nonmagnetic to a magnetic phase. Moreover, we show that the eigenstate ψadia of the infinitely strongly interacting system with |n1+n2|>2 and |n1-n2|<n (n1 and n2 denote the number of fermions of components 1 and 2, respectively), which is reached experimentally by adiabatically changing the system parameters, does not, as previously proposed, coincide with the wave function ψG obtained by applying a generalized Fermi-Fermi mapping function to the eigenfunction of the noninteracting single-component Fermi gas.