  We investigate a method for generating nonlinear phase shifts on
superpositions of photon number states. The light is stored in a Bose-Einstein
condensate via electromagnetically-induced transparency memory techniques. The
atomic collisions are exploited to generate a nonlinear phase shift of the
stored state. The stored light is then revived with the nonlinear phase shift
imprinted upon it. We show that this method can be used as a nonlinear-sign
gate in the regime where the Thomas-Fermi and mean-field approximations are
valid. We test these approximations using realistic parameters and find that
these approximations pass the standard tests for validity in a single-component
condensate. However, for the two-component condensates considered here, we find
that these conditions are insufficiently strict. We find a stronger set of
conditions and show for the same set of parameters that the approximations are
invalid.
