Example of a Quantum Anomaly in the Physics of Ultracold Gases

We propose an experimental scheme for the observation of a quantum anomaly---quantum-mechanical symmetry breaking--in a two-dimensional harmonically trapped Bose gas.\footnote{Maxim Olshanii, H\'{e}l\`{e}ne Perrin, Vincent Lorent, Phys.\ Rev.\ Lett. 105, 095302 (2010).} The anomaly manifests itself in a shift of the monopole excitation frequency away from the value dictated by the Pitaevskii-Rosch dynamical symmetry.\footnote{L. P. Pitaevskii and A. Rosch, Phys.\ Rev.\ A 55, R853 (1997).} While the corresponding classical Gross-Pitaevskii equation and the hydrodynamic equations derived from it 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.