Controlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances

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We report on a proposal to reduce the group velocity of a small ``laser'' Bose-Einstein condensate upon passing through a larger ``medium'' condensate of the same isotopic species in analogy to slowing of light passing through dispersive media. We make use of ultracold collisions near a magnetic Feshbach resonance, which gives rise to a sharp variation in scattering length with collision energy and thereby changes the group velocity. A generalized Gross-Pitaevskii equation is used to derive an expression for the group velocity in a homogeneous medium as well as for the spatial delay $\ensuremath{\delta}$, through a finite-sized medium BEC with a Thomas-Fermi density distribution. We predict a maximum reduction of the group velocity by a half, which physically corresponds to freely propagating Feshbach molecules. For typical narrow Feshbach resonances and a medium with number density ${10}^{15}$ cm${}^{\ensuremath{-}3}$, up to $85%$ of the lower bound can be achieved, making the effect experimentally observable. We also derive constraints on the experimental realization of our proposal.