Elementary excitations and universal interaction in Bose-Einstein condensates at large scattering lengths

Abstract

We present a theoretical analysis of excitation modes in Bose-Einstein condensates of ultracold alkali-metal gases for large scattering lengths, showing clear deviations from the Bogoliubov prediction as seen by Papp et al. [Phys. Rev. Lett. 101, 135301 (2008)]. We construct the atom-atom interaction by deriving the $T$ matrix of such systems from two coupled (open and closed) channels assuming that the Feshbach resonance dominates the latter. We calculate molecular bound-state energies as a function of the magnetic field and compare with available experiments. The $s$-wave phase shifts determine the local effective interaction with long-ranged repulsion and short-ranged attraction. We show that it becomes a universal function at large scattering lengths. Finally, we use this interaction to characterize the ground-state and elementary excitations of ${}^{85}$Rb, ${}^{87}$Rb, and ${}^{23}$Na gases. Good agreement with line shift experiments in ${}^{85}$Rb is achieved. We find that, at large scattering lengths, Bragg scattering experiments could directly measure the momentum dependence of the effective two-body potential.