Breathing mode frequencies of a rotating Fermi gas in the BCS-BEC crossover region

TL;DR

This paper investigates how the breathing mode frequencies of a rotating Fermi gas in the BCS-BEC crossover are affected by anharmonic trapping potentials, revealing conditions for mode merging and instability.

Contribution

It provides a detailed analysis of the impact of radial anharmonicity and rotation on breathing mode frequencies across the BCS-BEC crossover, identifying critical points for stability.

Findings

Mode frequencies increase or decrease with anharmonicity

Mode merging occurs at a critical anharmonicity leading to instability

Large chemical potential in BCS regime affects mode behavior

Abstract

We study the breathing mode frequencies of a rotating Fermi gas trapped in a harmonic plus radial quartic potential. We find that as the radial anharmonicity increases, the lowest order radial mode frequency increases while the next lowest order radial mode frequency decreases. Then at a critical anharmonicity, these two modes merge and beyond this merge the cloud is unstable against the oscillations. The critical anharmonicity depends on both rotational frequency and the chemical potential. As a result of the large chemical potential in the BCS regime, even with a weak anharmonicity the lowest order mode frequency increases with decreasing the attractive interaction. For large enough anharmonicities in the weak coupling BCS limit, we find that the excitation of the breathing mode frequencies make the atomic cloud unstable.