Behavior of quantum decoherence under bang-bang controls

Bang-bang(BB) decoupling schemes for low-level atom systems in the cases of adiabatic decoherence alone, amplitude decoherence alone, and the case of adiabatic and amplitude decoherence together have been fully discussed. And for arbitrary-level atom system in amplitude decoherence, BB decoupling scheme was also given. Here after a review, we give the BB decoupling scheme for an arbitrary-level atom system in general decoherence.