Generation of nonclassical states of light in the Bose – Einstein condensate under electromagnetically induced transparency

A quantum theory of the interaction of the atomic Bose condensate with external optical fields has been developed for a two-beam $\Lambda$-scheme close to resonance. Regimes have been obtained where the coefficients of Kerr nonlinearity and nonlinear absorption reach giant values and even become negative, which gives rise to the effect of nonlinear electromagnetically induced transparency. The possibility of the efficient generation of quadrature-squeezed light under the condition of the nonlinear compensation of optical losses has been shown.