Scattering of two heavy Fermi polarons: resonances and quasibound states

TL;DR

This paper explores how two heavy Fermi polarons interact in a Fermi gas, revealing resonances and quasibound states linked to Efimov physics, with implications for impurity interactions in quantum many-body systems.

Contribution

It provides a theoretical analysis of scattering properties and phase shifts between two heavy impurities, highlighting the emergence of Efimov-related resonances and quasibound states in a Fermi medium.

Findings

Resonances occur at the continuum threshold when Efimov states appear.

Induced scattering length changes sign at resonance points.

Efimov states can become quasibound with finite decay widths.

Abstract

Impurities in a Fermi sea, or Fermi polarons, experience a Casimir interaction induced by quantum fluctuations of the medium. When there is short-range attraction between impurities and fermions, also the induced interaction between two impurities is strongly attractive at short distance and oscillates in space for larger distances. We theoretically investigate the scattering properties and compute the scattering phase shifts and scattering lengths between two heavy impurities in an ideal Fermi gas at zero temperature. While the induced interaction between impurities is weakly attractive for weak impurity-medium interactions, we find that impurities strongly and attractively interacting with the medium exhibit resonances in the induced scattering with a sign change of the induced scattering length and even strong repulsion. These resonances occur whenever a three-body Efimov bound state appears at the continuum threshold. At energies above the continuum threshold, we find that the Efimov state in medium can turn into a quasibound state with a finite decay width.