  The dynamics of entanglement and quantum discord between two identical qubits
strongly interacting with a common single mode leaky cavity field have been
investigated beyond the rotating wave approximation (RWA) by using recently
derived Lindblad type quantum optical master equation [F. Beaudoin, J.M.
Gambetta, A. Blais, Phys. Rev. A {\bf 84}, 043832 (2011)] that can describe the
losses of the cavity field in a strong atom-field coupling regime. Contrary to
previous investigations of the same model in the dissipative regime by using
the standard Lindblad quantum optical master equation in a strong-coupling
regime, the atom-field steady states are found to be cavity decay rate
independent and have a very simple structure determined solely by the overlap
of initial atomic state with the subradiant state which is valid for all
coupling regimes. Non-RWA dynamics are found to have remarkable effects on the
steady state quantum discord and entanglement that cannot be achieved under RWA
conditions, for instance, they can induce steady state entanglement even for
the initial states that have no overlap with the subradiant state. Moreover,
the non-RWA dynamics are found to reverse the initial state dependence of
steady state entanglement and quantum discord contrary to the RWA case.
