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Magnetic impurity in a one-dimensional few-fermion system

Lukas Rammelmüller, David Huber, Matija Čufar, Joachim Brand, Hans-Werner Hammer, Artem G. Volosniev

SciPost Phys. 14, 006 (2023) · published 24 January 2023

Abstract

We present a numerical analysis of spin-$\tfrac{1}{2}$ 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 $s$-wave 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.

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