  We investigate steady-state entanglement (SSE) between two nitrogen-vacancy
(NV) centers in distant nanodiamonds on an ultrathin Yttrium Iron Garnet (YIG)
strip. We determine the dephasing and dissipative interactions of the qubits
with the quanta of spin waves (magnon bath) in the YIG depending on the qubit
positions on the strip. We show that the magnon's dephasing effect can be
eliminated, and we can transform the bath into a multimode displaced thermal
state using external magnetic fields. Entanglement dynamics of the qubits in
such a displaced thermal bath have been analyzed by deriving and solving the
master equation. An additional electric field is considered to engineer the
magnon dispersion relation at the band edge to control the Markovian character
of the open system dynamics. We determine the optimum geometrical parameters of
the system of distant qubits and the YIG strip to get SSE. Furthermore,
parameter regimes for which the shared displaced magnon bath can sustain
significant SSE against the local dephasing and decoherence of NV centers to
their nuclear spin environments have been determined. Along with SSE, we
investigate the steady-state coherence (SSC) and explain the physical mechanism
of how delayed SSE appears following a rapid generation and sudden death of
entanglement using the interplay of decoherence-free subspace states, system
geometry, displacement of the thermal bath, and enhancement of the qubit
dissipation near the magnon band edge. A non-monotonic relation between bath
coherence and SSE is found, and critical coherence for maximum SSE is
determined. Our results illuminate the efficient use of system geometry, band
edge in bath spectrum, and reservoir coherence to engineer system-reservoir
interactions for robust SSE and SSC.
