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.
