Symmetries and decoherence of two-component confined atomic clouds: Study of the atomic echo in the two-component Bose-Einstein condensate

Implications of the internal symmetries on the dynamics of the trapped two-component atomic vapors are discussed. In the cases of Rb-87 (bosons) as well as of K-40 (fermions) trapped in the two hyperfine states, the intrinsic su(2) symmetry can be realized with a very good precision. Such a symmetry protects the global operators, which are the generators of the symmetry, from any decoherence. The case of boson-fermion mixture is discussed as well. The role of external factors, breaking the symmetry, in inducing the decoherence of the global operators is considered. It is shown that, the loss of the correlations is not faster than the rates of the induced heating or losses, provided the noise is characterized by short correlation length. The case of the extrinsic long-ranged fluctuations is also considered. Intrinsic mechanisms of decoherence of the correlators of the condensate operators of the two-component condensate are analyzed. The atomic echo is discussed as a test for the reversibility of the phase diffusion effect. The intensity and the profile of the multiple echo are calculated numerically as well as analytically.