Cloud shape of a molecular Bose-Einstein condensate in a disordered trap: a case study of the dirty boson problem

TL;DR

This study combines experiments and theory to analyze the shape of a molecular Bose-Einstein condensate in disordered traps, revealing agreement at low disorder and discrepancies at high disorder, highlighting the limits of current approximations.

Contribution

It provides a comprehensive comparison of experimental measurements with non-perturbative and perturbative theories for disordered Bose-Einstein condensates, identifying the regime where theories succeed or fail.

Findings

Quantitative agreement with perturbative theory at low disorder

Perfect reproduction of geometric mean of widths at strong disorder

Systematic deviation of cloud aspect ratio with increasing disorder

Abstract

We investigate, both experimentally and theoretically, the static geometric properties of a harmonically trapped Bose-Einstein condensate of ${}^6$Li$_2$ molecules in laser speckle potentials. Experimentally, we measure the in-situ column density profiles and the corresponding transverse cloud widths over many laser speckle realizations. We compare the measured widths with a theory that is non-perturbative with respect to the disorder and includes quantum fluctuations. Importantly, for small disorder strengths we find quantitative agreement with the perturbative approach of Huang and Meng, which is based on Bogoliubov theory. For strong disorder our theory perfectly reproduces the geometric mean of the measured transverse widths. However, we also observe a systematic deviation of the individual measured widths from the theoretically predicted ones. In fact, the measured cloud aspect ratio monotonously decreases with increasing disorder strength, while the theory yields a constant ratio. We attribute this discrepancy to the utilized local density approximation, whose possible failure for strong disorder suggests a potential future improvement.