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We investigate, both experimentally and theoretically, the static geometricproperties of a harmonically trapped Bose-Einstein condensate of ${}^6$Li$_2$molecules in laser speckle potentials. Experimentally, we measure the in-situcolumn density profiles and the corresponding transverse cloud widths over manylaser speckle realizations. We compare the measured widths with a theory thatis non-perturbative with respect to the disorder and includes quantumfluctuations. Importantly, for small disorder strengths we find quantitativeagreement with the perturbative approach of Huang and Meng, which is based onBogoliubov theory. For strong disorder our theory perfectly reproduces thegeometric mean of the measured transverse widths. However, we also observe asystematic deviation of the individual measured widths from the theoreticallypredicted ones. In fact, the measured cloud aspect ratio monotonously decreaseswith increasing disorder strength, while the theory yields a constant ratio. Weattribute this discrepancy to the utilized local density approximation, whosepossible failure for strong disorder suggests a potential future improvement.

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