Diffusive expansion of a dipolar Bose–Einstein condensate in three-dimensional disorder potentials

We study the effects of dipole–dipole interactions on the diffusion of an expanding atomic Bose–Einstein condensate with tunable s-wave interactions in three-dimensional disorder potentials. First-order correction due to local and nonlocal nonlinearities to the average atomic density is analytically calculated in the long expanding time limit using a perturbative theory. It is found that the diffusion coefficient exhibits a stronger anisotropy dependence due to the dipolar interactions. We show that the intriguing interplay of dipolar and nondipolar interactions and disorder potential may affect the diffusive expansion. Graphical Abstract Profiles of the dynamics of the average atomic density of attractive DDI from Eq .(19) for different values of $$\epsilon _{dd}$$ ϵ dd and $$p=0.08$$ p = 0.08 . Black lines: $$\epsilon _{dd}=0$$ ϵ dd = 0 . Red lines: $$\epsilon _{dd}=0.16$$ ϵ dd = 0.16 . Blue lines: $$\epsilon _{dd}=0.4$$ ϵ dd = 0.4 . Green lines: $$\epsilon _{dd}=0.8$$ ϵ dd = 0.8