Quantum oscillations and entanglement in Aharonov–Bohm rings with two magnetic impurities and asymmetric electron injection

We study spin-polarized transport through an Aharonov–Bohm ring threaded by magnetic flux, which is serially or laterally coupled to an external waveguide. The ring contains two magnetic impurities, whose spins are coupled to the electron spin through contact spin–spin interactions. In the framework of a quantum waveguide approach, asymmetry effects in the coupling of the ring to the environment are taken into account through a suitable, unitary parametrization of the vertex scattering operator, containing an asymmetry parameter λ and a coupling parameter ϵ. For λ=1, ϵ=4/9 this parametrization gives the same results as the employment of Griffithʹs boundary conditions. We find that asymmetry may considerably influence the transmission of maximally entangled states through the ring. To this end, we analyze both the Aharonov–Bohm oscillations of the transmission coefficients, and the entanglement between the impurities spins by means of concurrencies. We show that asymmetry is less influential in the side-coupled configuration, with respect to the serial case.