Ballistic spin rotator based on a Π nanojunction with spin-orbit interaction

In a quantum nanojunction with a Pi geometry and two external leads, the spin properties of an incoming electron are modified by the spin-orbit interaction, resulting in a transformation of the spin polarization of the injected current. The Pi nanojunction acts as a ballistic spin rotator whose properties can be varied by tuning the Rashba parameter of the spin-orbit interaction, by changing the relative position of the junctions, as well as by the length of the transverse legs. We show that a large class of unitary transformations can be attained with already one Pi nanojunction or a few Pi nanojunctions in series. By choosing appropriate parameters the spin transformations can be made unitary, which corresponds to lossless gates.