# Small amplitude collective modes of a finite-size unitary Fermi gas in deformed traps

## TL;DR

This study explores the collective breathing modes of a finite-size unitary Fermi gas in deformed traps, revealing how trap shape and size influence oscillation frequencies and flow patterns, with implications for experimental investigations.

## Contribution

It introduces a combined SLDA and QRPA approach to analyze how trap deformation and size affect collective modes in a unitary Fermi gas, highlighting finite size effects.

## Key findings

- Large pairing strength shifts oscillation frequencies.
- Deformation affects flow patterns of collective modes.
- Finite size effects diminish as system size increases.

## Abstract

We have investigated collective breathing modes of a unitary Fermi gas in deformed harmonic traps. The ground state is studied by the Superfluid Local Density Approximation (SLDA) and small-amplitude collective modes are studied by the iterative Quasiparticle Random Phase Approximation (QRPA). The results illustrate the evolutions of collective modes of a small system in traps from spherical to elongated or pancake deformations. For small spherical systems, the influences of different SLDA parameters are significant, and, in particular, a large pairing strength can shift up the oscillation frequency of collective mode. The transition currents from QRPA show that the compressional flow patterns are nontrivial and dependent on the deformation. Finally, the finite size effects are demonstrated to be reasonable when progressing towards larger systems. Our studies indicate that experiments on small and medium systems are valuable for understanding effective interactions in systems with varying sizes and trap deformations.