Entanglement generation in two-dimensional quantum waveguides with magnetic impurities

We study spin-dependent transport in a two-dimensional waveguide with two magnetic impurities. The waveguide may have a non-trivial boundary, and the electron is coupled to the defects through contact spin–spin interactions amended by a suitable form factor to avoid divergences in the transverse-mode expansion. The scattering operator is evaluated in a fully multi-channel framework, and entanglement production analyzed by studying both the transmission coefficients, and the concurrence between the defects' spin degrees of freedom. For non-entangled incoming states, entanglement production is enhanced in correspondence to resonance transmission. Differently from one-dimensional, single-channel scattering, however, no tendency toward robust entanglement production is observed with increasing energy. On the other hand, the peculiar role played by the maximally entangled singlet state of the impurities in electron transmission is confirmed in these multi-channel calculations. In this case also, the whole scenario is significantly more complex than in strictly one-dimensional systems, because of the opening of thresholds with increasing energy, and the presence of evanescent modes, whose effects cannot be ignored.