The axial breathing mode in rapidly rotating Bose-Einstein condensates and uncertainty of the rotation velocity

Experiments on the axial breathing mode in a rapidly rotating Bose-Einstein condensate are examined. Assuming a cold cloud without thermal component, we show that errors due to defocus of an imaging camera in addition to an inclination of the rotational axis can lead to a significant underestimate of the rotation rate in the fast rotation limit; within these uncertainties, our theoretical prediction agrees with the experimental data. We also show that, in the fast rotation regime, the Thomas-Fermi theory, which is inapplicable there, underestimates the rotation rate. Underestimate of the rotation rate due to these effects would also partly explain a discrepancy between theory and experiment for the Tkachenko mode frequency in the fast rotation regime.