Decoherence slowing down in a symmetry-broken environment

We show how to characterize the temporal evolution of a single qubit interacting with a thermal bath by correlation functions of the bath under quite general hypotheses. The aim is to show how the qubit decoherence time depends on the degree of correlation of the bath. We explicitly study some spin-bath models where every spin of the environment interacts with the qubit either directly or by the mediation of a harmonic oscillator. In both cases we find an increase of the decoherence time as soon as a symmetry breaking occurs in the environment. In the latter case a possible experimental setup is discussed.