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

TL;DR

This paper investigates how imaging errors and theoretical limitations affect the measurement of rotation rates in rapidly rotating Bose-Einstein condensates, highlighting uncertainties in experimental and theoretical approaches.

Contribution

It identifies sources of error in measuring rotation velocity and clarifies the limitations of Thomas-Fermi theory in the fast rotation regime.

Findings

Imaging defocus and axis inclination cause significant underestimation of rotation rates.

Thomas-Fermi theory underestimates rotation rates in the fast rotation regime.

Uncertainties may explain discrepancies in Tkachenko mode frequency measurements.

Abstract

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.