Spin polarization of entangled and mixed electron states in a beam splitter geometry coupled to an electron reservoir

We study the spin polarization of mixed and entangled electron states in a four-probe/beam splitter geometry with local Rashba and Dresselhaus interactions. A pair of maximally entangled electrons collides with the beam splitter and enters into two perpendicular branches of length L, composed of spin-orbit active materials (gate-confined two-dimensional electron gas). One of the branches is connected to an electron reservoir that acts as a source of decoherence by either behaving as a voltage probe or as a controlled source or sink of current at fixed voltage. Such a decoherence source is used to modify the entropy of an unpolarized incoming state in order to generate electron polarization at one or both output branches. The degree of entanglement of the global state and the spin polarization is computed for the outgoing electrons as a function of the coupling to the electron reservoir. Experimentally available spin-orbit strength at the beam splitter arms, for arm lengths of a few micrometers, is able to modulate spin polarization up to 80% in particular spin axes. The Dresselhaus and Rashba coefficients play a symmetric role in modulating the polarization. Significantly less polarization is achieved for incoming mixed states due to the local operation of the reservoir.