Magnetic impurity in a one-dimensional few-fermion system

Abstract

We present a numerical analysis of spin-$\frac{1}{2}$ 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.

SciPost Submission

References in corpus (21)

• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Recent developments in no-core shell-model calculations
• An exactly solvable model of the BCS-BEC crossover
• Evidence of topological Shiba bands in artificial spin chains on superconductors
• Controlled length-dependent interaction of Majorana modes in Yu-Shiba-Rusinov chains
• The FFLO state in the one-dimensional attractive Hubbard model and its fingerprint in the spatial noise correlations
• Observation of Cooper Pairs in a Mesoscopic 2D Fermi Gas
• Spectrum and Dynamics of the BCS-BEC crossover from a few-body perspective
• Quantum magnetism in strongly interacting one-dimensional spinor Bose systems
• One-dimensional Fermi gas with a single impurity in a harmonic trap: Perturbative description of the upper branch
• Pairing of few Fermi atoms in one dimension
• A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
• Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement
• Heavy polarons in ultracold atomic Fermi superfluids at the BEC-BCS crossover: formalism and applications
• Bound states of a localized magnetic impurity in a superfluid of paired ultracold fermions
• Quantum magnetism and topological superconductivity in Yu-Shiba-Rusinov chains
• Tunneling processes between Yu-Shiba-Rusinov bound states
• Improved walker population control for full configuration interaction quantum Monte Carlo
• Spatial noise correlations of a chain of ultracold fermions - A numerical study
• Signatures of the BCS-BEC crossover in the yrast spectra of Fermi quantum rings
• Pairing patterns in polarized unitary Fermi gases above the superfluid transition

Cited by in corpus (8)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• A modular implementation of an effective interaction approach for harmonically trapped fermions in 1D
• Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons
• Comparison of renormalized interactions using one-dimensional few-body systems as a testbed
• Few particles with an impurity in a one-dimensional harmonic trap
• Sourced Carrollian Fluids Dual to Black Hole Horizons
• Effective theory for strongly attractive one-dimensional fermions
• Composite Bosons Superposition Ansatz Approach to One-Dimensional Trapped Few-Fermion Systems