# Long range mediated interactions in a mixed dimensional system

## TL;DR

This paper proposes a mixed-dimensional atomic gas system to detect mediated interactions through measurable frequency shifts in coupled fermionic clouds, providing a new experimental probe for such interactions.

## Contribution

It introduces a novel mixed-dimensional setup and a strong coupling theoretical framework to systematically study mediated interactions in atomic gases.

## Key findings

- Frequency shift of dipole oscillations is a measurable indicator of mediated interactions.
- Strong interactions significantly enhance the frequency shift, making detection feasible.
- The theoretical model accurately accounts for two-body mixed-dimensional scattering effects.

## Abstract

We present a mixed-dimensional atomic gas system to unambiguously detect and systematically probe mediated interactions. In our scheme, fermionic atoms are confined in two parallel planes and interact via exchange of elementary excitations in a three-dimensional background gas. This interaction gives rise to a frequency shift of the out-of-phase dipole oscillations of the two clouds, which we calculate using a strong coupling theory taking the two-body mixed-dimensional scattering into account exactly. The shift is shown to be easily measurable for strong interactions and can be used as a probe for mediated interactions.