Nonlinear interaction of light with a Bose-Einstein condensate: Methods to generate sub-Poissonian light

We consider a Λ-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 the strong nonlinearity. An effective two-level quantum model of the system is derived and studied. Our approach is based on a possibility of establishing a connection of the underlying algebra with the su(2) algebra within the formalism of the polynomial algebras of excitations (PAE). We propose an efficient way for the generation of sub-Poissonian 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.