Few-Body Perspective of a Quantum Anomaly in Two-Dimensional Fermi Gases

A quantum anomaly manifests itself in the deviation of the breathing mode frequency from the scale invariant value of 2ω in two-dimensional harmonically trapped Fermi gases, where ω is the trapping frequency. Its recent experimental observation with cold atoms reveals an unexpected role played by the effective range of interactions, which requires a quantitative theoretical understanding. Here we provide accurate, benchmark results on a quantum anomaly from a few-body perspective. We consider the breathing mode of a few trapped interacting fermions in two dimensions up to six particles and present the mode frequency as a function of scattering length for a wide range of effective range. We show that the maximum quantum anomaly gradually reduces as the effective range increases while the maximum position shifts towards the weak-coupling limit. We extrapolate our few-body results to the many-body limit and find a good agreement with the experimental measurements. Our results may also be directly applicable to a few-fermion system prepared in microtraps and optical tweezers.