An Example of Quantum Anomaly in the Physics of Ultra-Cold Gases

TL;DR

This paper proposes an experimental method to observe a quantum anomaly in a 2D Bose gas, where quantum effects break classical symmetry, leading to measurable shifts in excitation frequencies.

Contribution

It introduces an experimental scheme to detect quantum anomalies in ultra-cold gases by measuring shifts in monopole excitation frequencies.

Findings

Quantum anomaly causes a ~1% frequency shift.

Classical equations exhibit symmetry, but quantum effects break it.

Proposed method uses dipole oscillations as a frequency gauge.

Abstract

In this article, we propose an experimental scheme for observation of a quantum anomaly---quantum-mechanical symmetry breaking---in a two-dimensional harmonically trapped Bose gas. The anomaly manifests itself in a shift of the monopole excitation frequency away from the value dictated by the Pitaevskii-Rosch dynamical symmetry [L. P. Pitaevskii and A. Rosch, Phys. Rev. A, 55, R853 (1997)]. While the corresponding classical Gross-Pitaevskii equation and the derived from it hydrodynamic equations do exhibit this symmetry, it is---as we show in our paper---violated under quantization. The resulting frequency shift is of the order of 1% of the carrier, well in reach for modern experimental techniques. We propose using the dipole oscillations as a frequency gauge.