  We consider $\Lambda$-type model of the Bose-Einstein condensate of sodium
atoms interacting with the light. Coefficients of the Kerr-nonlinearity in the
condensate can achieve large and negative values providing the possibility for
effective control of group velocity and dispersion of the probe pulse. We find
a regime when the observation of the "slow" and "fast" light propagating
without absorption becomes achievable due to strong nonlinearity. An effective
two-level quantum model of the system is derived and studied based on the su(2)
polynomial deformation approach. We propose an efficient way for generation of
subpoissonian fields in the Bose-Einstein condensate at time-scales much
shorter than the characteristic decay time in the system. We show that the
quantum properties of the probe pulse can be controlled in BEC by the classical
coupling field.
