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 $N_2-N_1$ induced by an rf-field in the two-component atomic cloud characterized by equal scattering lengths. This situation is very close to the actual JILA experiments with the two-component ${}^{87}$Rb vapor. We show that no intrinsic decoherence exists for $N_2-N_1$, provided the exact SU(2) symmetry holds. This contrasts with finite dissipation of the normal modes even in the presence of the SU(2) symmetry. The intrinsic decoherence for $N_2-N_1$ may occur as long as deviations from the exact SU(2) symmetry are taken into account. Such decoherence, however, should be characterized by very long times governed by the smallness of the deviations from the symmetry. We suggest testing the evolution of $N_2-N_1$ by conducting echo-type experiments.