Title: Repulsive Fermi polarons with negative effective mass,
Abstract: Recent LENS experiment on a 3D Fermi gas has reported a negative effective
mass ($m^*<0$) of Fermi polarons in the strongly repulsive regime. There
naturally arise a question whether the negative $m^*$ is a precursor of the
instability towards phase separation (or itinerant ferromagnetism). In this
work, we make use of the exact solutions to study the ground state and
excitation properties of repulsive Fermi polarons in 1D, which can also exhibit
a negative $m^*$ in the super Tonks-Girardeau regime. By analyzing the total
spin, quasi-momentum distribution and pair correlations, we conclude that the
negative $m^*$ is irrelevant to the instability towards ferromagnetism or phase
separation, but rather an intrinsic feature of collective excitations for
fermions in the strongly repulsive regime. Surprisingly, for large and negative
$m^*$, such excitation is accompanied with a spin density modulation when the
majority fermions move closer to the impurity rather than being repelled far
away, contrary to the picture of phase separation. These results suggest an
alternative interpretation of negative $m^*$ as observed in recent LENS
experiment.