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

2010/06/30 by Maxim Olshanii, Hélène Perrin, Vincent Lorent · 1 citation
Physics and Astronomy · #cond-mat.quant-gas #quant-ph

paper · pdf · doi:10.1103/physrevlett.105.095302

published as Phys. Rev. Lett. 105, 095302 (2010) · Misprints corrected, a discussion on damping added, text is polished and shortened. 5 pages, 1 figure

arxiv created 2011/01/13 · arxiv updated 2015/05/19

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.

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