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We present highly-accurate energy spectra and eigen functions of small 1dharmonically trapped two-component Fermi gases with interspecies$\delta$-function interactions, and analyze the correlations of the so-calledupper branch (i.e., the branch that describes a repulsive Fermi gas consistingof atoms but no molecules) for positive and negative coupling constants.Changes of the two-body correlations as a function of the interspecies couplingstrength reflect the competition of the interspecies interaction and theeffective repulsion due to the Pauli exclusion principle, and are interpretedas a few-body analog of a transition from a non-magnetic to a magnetic phase.Moreover, we show that the eigenstate $\psi_{\rm{adia}}$ of the infinitelystrongly-interacting system with $|n_1+n_2|>2$ and $|n_1-n_2| < n$ ($n_1$ and$n_2$ denote the number of fermions of components 1 and 2, respectively), whichis reached experimentally by adiabatically changing the system parameters, doesnot, as previously proposed, coincide with the wave function $\psi_{\rm{G}}$obtained by applying a generalized Fermi-Fermi mapping function to the eigenfunction of the non-interacting single-component Fermi gas.

Correlations of the upper branch of 1d harmonically trapped two-component Fermi gases