In the framework of the nonlinear lambda model we investigate propagation of solitons in atomic vapors and Bose-Einstein condensates. We show how the complicated nonlinear interplay between fast solitons and slow-light solitons in the lambda-type media points to the possibility to create optical gates and, thus, to control the optical transparency of the lambda-type media. We provide an exact analytic description of decelerating, stopping and reaccelerating of slow-light solitons in atomic media in the nonadiabatic regime. Dynamical control over slow-light solitons is realized via a controlling field generated by an auxiliary laser. For a rather general time dependence of the field; we find the dynamics of the slow-light soliton inside the medium. We provide an analytical description for the nonlinear dependence of the velocity of the signal on the controlling field. If the background field is turned off at some moment of time, the signal stops. We find the location and shape of the spatially localized memory bit imprinted into the medium. We discuss physically interesting features of our solution, which are in a good agreement with recent experiments.

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An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. sun(2), algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N -atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of N atoms in a resonator is found to result from collective effects.

We propose a method to control the optical transparency of a Bose-Einstein condensate with working energy levels of the Λ-type. The reported effects are essentially nonlinear and are considered in the framework of an exactly solvable model describing the interaction of light with a Λ-type medium. We show how the complicated nonlinear interplay between fast and slow solitons in the Λ-type medium points to a possibility to create optical gates as well as to a possibility to store optical information.

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