Bose-Einstein Condensates in Strongly Disordered Traps

A Bose-Einstein condensate in an external potential consisting of a superposition of a harmonic and a random potential is considered theoretically. From a semiquantitative 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 findings are generalized to anisotropic traps.

Figure 1

Condensate radius as a function of the particle number. The bold line corresponds to the equilibrium fragmented state, and the dashed line corresponds to the metastable single connected state.

Figure 2

State of dense fragments. Each fragment includes $\mathcal{L}/a$ particles. The minimal condensate radius is $R_F\sim (Na{)}^{1/3}{\mathcal{L}}^{2/3}$.