# Low-energy modes of spin-imbalanced Fermi gases in BCS phase

## TL;DR

This paper investigates the low-energy collective excitations in spin-imbalanced superfluid Fermi gases within the BCS regime, revealing how population imbalance and temperature influence mode behavior and system stability.

## Contribution

It provides a detailed analysis of how spin imbalance and temperature affect collective modes and identifies signs of phase instability in the system.

## Key findings

- Imbalance shifts mode frequency lower and increases damping.
- Temperature has minimal effect on mode frequency and damping.
- Zero-frequency modes indicate phase separation instability.

## Abstract

The low-energy modes of a spin-imbalanced superfluid Fermi gas in the Bardeen-Cooper-Schrieffer (BCS) side are studied. The gas is assumed to be sufficiently dilute so that the pairing of atoms can be considered effective only in s-wave between fermions of different internal state. The order parameter at equilibrium is determined by the mean-field approximation, while the properties of the collective modes are calculated within a Gaussian approximation for the fluctuations of the order parameter. In particular we investigate the effects of asymmetry between the populations of the two different components and of temperature on the frequency and damping of collective modes. It is found that the temperature does not much affect the frequency and the damping of the modes, whereas an increase of the imbalance shifts the frequency toward lower values and enhances the damping sensitively. Besides the Bogoliubov-Anderson phonons, we observe modes at zero frequency for finite values of the wave-number. These modes indicate that an instability develops driving the system toward two separate phases, normal and superfluid.