Reduced quantum anomaly in a quasi-2D Fermi superfluid: The significance of the confinement-induced effective range of interactions

TL;DR

This paper shows that the quantum anomaly in a quasi-2D Fermi superfluid is weaker than expected due to the confinement-induced effective range of interactions, aligning theory with experimental results.

Contribution

It demonstrates that including the confinement-induced effective range of interactions explains the reduced quantum anomaly in quasi-2D Fermi gases.

Findings

Quantum anomaly is weaker than 10% in experiments.

Confinement-induced effective range explains the anomaly reduction.

Simple 2D models are insufficient for accurate descriptions.

Abstract

A two-dimensional (2D) harmonically trapped interacting Fermi gas is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale invariant value $\omega_{B}=2\omega_{\perp}$, where $\omega_{\perp}$ is the trapping frequency. The predicted maximum quantum anomaly ($\sim10\%$) has not been confirmed in experiments. Here, we theoretically investigate the zero-temperature density equation of state and the breathing mode frequency of an interacting Fermi superfluid at the dimensional crossover from three to two dimensions. We find that the simple model of a 2D Fermi gas with a single $s$-wave scattering length is not adequate to describe the experiments in the 2D limit, as commonly believed. A more complete description of quasi-2D leads to a much weaker quantum anomaly, consistent with the experimental observations. We clarify that the reduced quantum anomaly is due to the significant confinement-induced effective range of interactions, which is overlooked in previous theoretical and experimental studies.