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Quantum dynamics of a collection of atoms subjected to phase modulation hasbeen carefully revisited. We present an exact analysis of the evolution of atwo-level system (represented by a spinor) under the action of a time-dependentmatrix Hamiltonian. The dynamics is shown to evolve on two coupled potentialenergy surfaces, one of them binding while the other one scattering type. Thedynamics is shown to be quasi-integrable with nonlinear resonances. The boundeddynamics with intermittent scattering at random moments presents the scenarioreminiscent to Anderson and dynamical localization. We believe that a carefulanalytical investigation of a multi-component system which is classicallynon-integrable is relevant to many other fields, including quantum computationwith multi-qubit system.

Quasi-integrability and nonlinear resonances in cold atoms under modulation