Decoherence dynamics of interacting qubits coupled to a bath of local   optical phonons
  We study decoherence in an interacting qubit system described by infinite range Heisenberg model (IRHM) in a situation where the system is coupled to a bath of local optical phonons. Using perturbation theory in polaron frame of reference, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under non-adiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM upto leading orders of perturbation and thus has the same eigenstates as the IRHM. Using a quantum master equation with Markovian approximation of dynamical evolution, we show that the off diagonal elements of the density matrix donot decay in the energy eigen basis of IRHM. 
Muzaffar Qadir Lone and Sudhakar Yarlaggada
quant-ph cond-mat.str-el