Breathing mode frequency of a strongly interacting Fermi gas across the 2D-3D dimensional crossover

TL;DR

This paper investigates how the breathing mode frequency of a strongly interacting Fermi gas varies across the 2D to 3D dimensional crossover, considering quantum anomalies and trapping potentials using advanced theoretical methods.

Contribution

It introduces a beyond mean-field Gaussian pair fluctuation approach combined with sum-rule calculations to analyze the dimensional crossover effects on breathing mode frequencies.

Findings

Breathing mode frequency varies with dimensionality and interaction strength.

Quantum anomaly influences the breathing mode in 2D regimes.

Predictions are relevant for ultracold Fermi gases of $^{6}$Li and $^{40}$K.

Abstract

We address the interplay between dimension and quantum anomaly on the breathing mode frequency of a strongly interacting Fermi gas harmonically trapped at zero temperature. Using a beyond mean-field, Gaussian pair fluctuation theory, we employ periodic boundary conditions to simulate the dimensionality of the system and impose a local density approximation, with two different schemes, to model different trapping potentials in the tightly-confined axial direction. By using a sum-rule approach, we compute the breathing mode frequency associated with a small variation of the trapping frequency along the weakly-confined transverse direction, and describe its behavior as functions of the dimensionality, from two- to three-dimensions, and of the interaction strength. We compare our predictions with previous calculations on the two-dimensional breathing mode anomaly and discuss their possible observation in ultracold Fermi gases of $^{6}$Li and $^{40}$K atoms.