# Tunable zero and first sounds in ultracold Fermi gases with Rabi coupling

## TL;DR

This paper investigates how Rabi coupling influences zero and first sound propagation in ultracold Fermi gases, analyzing their dependence on interaction strength and external trapping, with implications for experimental setups.

## Contribution

It provides a theoretical analysis of zero and first sound in Rabi-coupled Fermi gases across different dimensions, incorporating effects of interactions and trapping potentials.

## Key findings

- Zero and first sound speeds depend on Rabi coupling and interaction strength.
- The study distinguishes between collisional and collisionless sound regimes.
- Density profiles are affected by harmonic trapping potentials.

## Abstract

We consider a weakly-interacting fermionic gas of alkali-metal atoms characterized by two hyper- fine states which are Rabi coupled. By using a Hartree approximation for the repulsive interaction we determine the zero-temperature equation of state of this Fermi gas in D spatial dimensions (D = 1, 2, 3). Then, adopting the Landau-Vlasov equation and hydrodynamic equations, we investi- gate the speed of first sound and zero sound. We show that the two sounds, which occur respectively in collisional and collisionless regimes, crucially depend on the interplay between interaction strength and Rabi coupling. Finally, we discuss for some experimentally relevant cases the effect of a trapping harmonic potential on the density profiles of the fermionic system.