  We investigate analytically and numerically the steady-state entanglement and
coherence of two coupled qubits each interacting with a local boson or fermion
reservoir, based on the Bloch-Redfield master equation beyond the secular
approximation. We find that there is non-vanishing steady-state coherence in
the nonequilibrium scenario, which grows monotonically with the nonequilibrium
condition quantified by the temperature difference or chemical potential
difference of the two baths. The steady-state entanglement in general is a
non-monotonic function of the nonequilibrium condition as well as the bath
parameters in the equilibrium setting. We also find that weak inter-qubit
coupling and high base temperature or chemical potential of the baths can
strongly suppress the steady-state entanglement and coherence, regardless of
the strength of the nonequilibrium condition. On the other hand, the energy
detuning of the two qubits, when used in a compensatory way with the
nonequilibrium condition, can lead to significant enhancement of the
steady-state entanglement in some parameter regimes. In addition, the qubits
typically have a stronger steady-state entanglement when coupled to fermion
baths exchanging particle with the system than boson baths exchanging energy
with the system under similar conditions. We also discussed the possible
experimental realization of measuring the steady state entanglement and
coherence for coupled qubits systems in nonequilibrium environments. These
results offer some general guidelines for optimizing the steady-state
entanglement and coherence in the coupled qubit system and may find potential
applications in quantum information technology.
