Bose-Einstein Condensates in Strongly Disordered Traps

Abstract

A Bose-Einstein condensate in an external potential consisting of a superposition of a harmonic and a random potential is considered theoretically. From a semi-quantitative analysis we find the size, shape and excitation energy as a function of the disorder strength. For positive scattering length and sufficiently strong disorder the condensate decays into fragments each of the size of the Larkin length $\mathcal{L}$. This state is stable over a large range of particle numbers. The frequency of the breathing mode scales as $1/{\mathcal{L}}^2$. For negative scattering length a condensate of size $\mathcal{L}$ may exist as a metastable state. These finding are generalized to anisotropic traps.

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