Implications of SU(2) symmetry on the dynamics of population difference in the two-component atomic vapor

We present an exact many-body solution for the dynamics of the population difference N2-N1 induced by an rf field in the two-component atomic cloud characterized by equal scattering lengths. We show that no intrinsic decoherence occurs for N2-N1, provided that the exact intrinsic SU(2) symmetry holds. Decoherence for N2-N1 arises when deviations from the symmetry exist either in the scattering lengths or in the confining potentials. We suggest testing the evolution of N2-N1 by conducting echo-type experiments.