Decoherence in a spin-spin-bath model with environmental self-interaction

A low-temperature model system consisting of a central spin coupled to a spin-bath is studied to determine whether interaction among bath spins has an effect on central spin dynamics. In the absence of intra-environmental coupling, decoherence of the central spin is fast and irreversible. Strong intra-environmental interaction results in an effective decoupling of the central spin from the bath and suppression of decoherence. Weaker intra-environmental coupling reduces but does not eliminate decoherence. We argue that similar suppression of decoherence should be observed for electronic states of He impurities in silicon or diamond.