  We consider a dissipative evolution of parametrically-driven qubits-cavity
system under the periodical modulation of coupling energy between two
subsystems, which leads to the amplification of counterrotating processes. We
reveal a very rich dynamical behavior of this hybrid system. In particular, we
find that the energy dissipation in one of the subsystems can enhance quantum
effects in another subsystem. For instance, optimal cavity decay assists to
stabilize entanglement and quantum correlations between qubits even in the
steady state and to compensate finite qubit relaxation. On the contrary, energy
dissipation in qubit subsystem results in the enhanced photon production from
vacuum for strong modulation, but destroys both quantum concurrence and quantum
mutual information between qubits. Our results provide deeper insights to
nonstationary cavity quantum electrodynamics in context of quantum information
processing and might be of importance for dissipative quantum state
engineering.
