We report on a proposal to change the group velocity of a small Bose Einstein

Condensate (BEC) upon collision with another BEC 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-Pitaveskii equation is derived for a small BEC moving

through a larger stationary BEC. We denote the two condensates by laser and

medium BEC, respectively, to highlight the analogy to a laser pulse travelling

through a medium. We derive an expression for the group velocity in a

homogeneous medium as well as for the difference in distance, $\delta$, covered

by the laser BEC in the presence and absence of a finite-sized medium BEC with

a Thomas-Fermi density distribution. For a medium and laser of the same

isotopic species, the shift $\delta$ has an upper bound of twice the

Thomas-Fermi radius of the medium. For typical narrow Feshbach resonances and a

medium with number density $10^{15}$ cm$^{-3}$ up to 85% of the upper bound can

be achieved, making the effect experimentally observable. We also derive

constraints on the experimental realization of our proposal.