Magnetic impurity in a one-dimensional few-fermion system

We present a numerical analysis of spin-1 2 fermions in a one-dimensional harmonic potential in the presence of a magnetic point-like impurity at the center of the trap. The model represents a few-body analogue of a magnetic impurity in the vicinity of an swave superconductor. Already for a few particles we find a ground-state level crossing between sectors with different fermion parities. We interpret this crossing as a few-body precursor of a quantum phase transition, which occurs when the impurity breaks a Cooper pair. This picture is further corroborated by analyzing density-density correlations in momentum space. Finally, we discuss how the system may be realized with existing cold-atoms platforms.

Automated summary

We numerically analyze spin-1/2 fermions in a one-dimensional harmonic potential with a magnetic point-like impurity. Even for a few particles, we observe ground state level crossings between different fermion parities. We interpret this as a few-body precursor to a quantum phase transition, where the impurity breaks a Cooper pair. This interpretation is supported by analyzing density-density correlations in momentum space. Finally, we discuss the experimental realization of the system using existing cold-atom platforms.