Nonlinear interaction of light with Bose-Einstein condensate: new methods to generate subpoissonian light

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 sho…