  We investigate spontaneous and pumped entanglement of two level systems in
the vicinity of a photonic topological insulator interface, which supports a
nonreciprocal (unidirectional), scattering-immune and topologically-protected
surface plasmon polariton in the bandgap of the bulk material. To this end, we
derive a master equation for qubit interactions in a general three-dimensional,
nonreciprocal, inhomogeneous and lossy environment. The environment is
represented exactly, via the photonic Green function. The resulting
entanglement is shown to be extremely robust to defects occurring in the
material system, such that strong entanglement is maintained even if the
interface exhibits electrically-large and geometrically sharp discontinuities.
Alternatively, depending on the initial excitation state, using a
non-reciprocal environment allows two qubits to remain unentangled even for
very close spacing. The topological nature of the material is manifest in the
insensitivity of the entanglement to variations in the material parameters that
preserve the gap Chern number. Our formulation and results should be useful for
both fundamental investigations of quantum dynamics in nonreciprocal
environments, and technological applications related to entanglement in
two-level systems.
