Mediated interactions between ions in quantum degenerate gases

TL;DR

This paper investigates how quantum degenerate gases mediate interactions between trapped ions, revealing different distance-dependent behaviors and potential observable effects on ion phonon frequencies.

Contribution

It provides analytical and diagrammatic insights into mediated ion interactions in Bose and Fermi gases, including strong interaction effects and experimental implications.

Findings

Bose gas mediates a power-law and Yukawa interaction at different distances.

Fermi gas mediates a power-law at high density and RKKY at low density.

Induced interactions cause observable shifts in ion phonon frequencies.

Abstract

We explore the interaction between two trapped ions mediated by a surrounding quantum degenerate Bose or Fermi gas. Using perturbation theory valid for weak atom-ion interaction, we show analytically that the interaction mediated by a Bose gas has a power-law behaviour for large distances whereas it has a Yukawa form for intermediate distances. For a Fermi gas, the mediated interaction is given by a power-law for large density and by a Ruderman-Kittel-Kasuya-Yosida form for low density. For strong atom-ion interactions, we use a diagrammatic theory to demonstrate that the mediated interaction can be a significant addition to the bare Coulomb interaction between the ions, when an atom-ion bound state is close to threshold. Finally, we show that the induced interaction leads to substantial and observable shifts in the ion phonon frequencies.