Giant optical nonlinearity of an atomic Bose-Einstein condensate and low-threshold bistability

The polarization of an atomic Bose-Einstein condensate weakly excited by laser radiation at a nearly resonance frequency is determined. The coefficient of nonlinearity (cubic in field) in the refractive index of the condensate is calculated for the slow decay mode due to the spontaneous emission of excited atoms, as well as for the stationary mode, when the loss of atoms is compensated by the injection of atoms into the trap. In both cases, the cubic nonlinearity coefficients of the condensate are several orders of magnitude larger than the corresponding values for known nonlinear media. The conditions for observing hysteresis in an interferometer containing the condensate in the stationary state in the presence of an incident laser beam are specified.