Impurity coupled to an artificial magnetic field in a Fermi gas in a ring trap

TL;DR

This paper investigates how an impurity in a Fermi gas within a ring trap responds to an artificial magnetic field, revealing how interactions influence the impurity's effective mass and dynamics, with exact solutions via Bethe Ansatz.

Contribution

It provides an exact Bethe Ansatz analysis of impurity dynamics in a Fermi gas under an artificial magnetic flux, highlighting interaction-dependent effective mass behaviors.

Findings

Effective mass increases with repulsive interactions, saturating at the total system mass.

Attractive interactions lead to a polaron with twice the single-particle mass.

Resonant effective mass behavior observed in certain excited states.

Abstract

The dynamics of a single impurity interacting with a many particle background is one of the central problems of condensed matter physics. Recent progress in ultracold atom experiments makes it possible to control this dynamics by coupling an artificial gauge field specifically to the impurity. In this paper, we consider a narrow toroidal trap in which a Fermi gas is interacting with a single atom. We show that an external magnetic field coupled to the impurity is a versatile tool to probe the impurity dynamics. Using Bethe Ansatz (BA) we calculate the eigenstates and corresponding energies exactly as a function of the flux through the trap. Adiabatic change of flux connects the ground state to excited states due to flux quantization. For repulsive interactions, the impurity disturbs the Fermi sea by dragging the fermions whose momentum matches the flux. This drag transfers momentum from the impurity to the background and increases the effective mass. The effective mass saturates to the total mass of the system for infinitely repulsive interactions. For attractive interactions, the drag again increases the effective mass which quickly saturates to twice the mass of a single particle as a polaron of the impurity and one fermion is formed. For excited states with momentum comparable to number of particles, effective mass shows a resonant behavior. We argue that standard tools in cold atom experiments can be used to test these predictions.