Decoherence induced by interacting quantum spin baths

We study decoherence induced on a two-level system which is coupled to a one-dimensional quantum spin chain.We consider the cases where the dynamics of the chain is determined by the Ising, XY, or Heisenberg exchange Hamiltonians.This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices.As an example, we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath.We provide results which go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss with the number of bath spins to whom the system is coupled and describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength.Finally we establish a relation between decoherence and entanglement inside the bath.For the Ising and the XY models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent Density Matrix Renormalization Group.