Center motions of nonoverlapping condensates coupled by long-range dipolar interaction in bilayer and multilayer stacks

Abstract

We investigate the effect of anisotropic and long-range dipole-dipole interaction (DDI) on the center motions of nonoverlapping Bose-Einstein condensates in bilayer and multilayer stacks. In the bilayer, it is shown analytically that while DDI plays no role in the in-phase modes of center motions of condensates, out-of-phase mode frequency (${\ensuremath{\omega}}_{o}$) depends crucially on the strength of DDI (${a}_{d}$). At the small-${a}_{d}$ limit, ${\ensuremath{\omega}}_{o}^{2}({a}_{d})\ensuremath{-}{\ensuremath{\omega}}_{o}^{2}(0)\ensuremath{\propto}{a}_{d}$. In the multilayer stack, transverse modes associated with center motions of coupled condensates are found to be optical-phonon-like. At the long-wavelength limit, phonon velocity is proportional to $\sqrt{a}{}_{d}$.