Non-local interactions in Bose-Einstein Condensates

Abstract

Bose-Einstein Condensates (BECs) are treated theoretically using the mean field Gross- Pitaevskii (GP) equation. Instead of using the local (δ-function) psueudopotential to account for the symmetric s-wave scattering between bosons, we take an extended pseudopotential to account for the finite range of inter-boson interactions. Such a pseudopotential would give corrections on top of the GP equation with local interactions. We first propose the energy functional for such correction terms added to the local GP equation. We then study the effect of finite range of interactions on the vortex solution, soliton solution and the excitation spectrum in a BEC. We see that the additional length scale emerging from the range of the inter-Boson interactions plays a significant role in the aforementioned excitations.