Quantum interference and spin-orbit interaction in a one-dimensional mesoscopic semiconductor ring with one input and two output leads can act as a spin beam splitter. Different polarization can be achieved in the two output channels from an originally totally unpolarized incoming spin state, very much like in a Stern-Gerlach apparatus. We determine the relevant parameters such that the device has unit efficiency.Comment: 4 pages, 3 figures; minor change

An array of quantum rings with local (ring by ring) modulation of the spin orbit interaction (SOI) can lead to novel effects in spin state transformation of electrons. It is shown that already small (3 × 3, 5 × 5) networks are remarkably versatile from this point of view: Working in a given network geometry, the input current can be directed to any of the output ports, simply by changing the SOI strengths by external gate voltages. Additionally, the same network with different SOI strengths can be completely analogous to the Stern-Gerlach device, exhibiting spatial-spin entanglement. PACS numbers:Using the spin degree of freedom in information processing applications has become an important and rapidly developing field. For most of the spintronic devices, spin is a classical resource, logical states are "up" and "down" with respect to certain quantization directions, but their superpositions play no role. On the other hand, the electron spin degree of freedom can also be considered one of the prospective carriers of qubits, the fundamental units in quantum information processing [1]. To realize this aim, however, requires to perform basic spin operations such as the production of spin-polarized carriers and spin rotation. Here we propose a device that can serve multiple purposes including the delivery of spinpolarized currents and rotating the spin direction, but it can also direct the input current into a given output port in a spin independent way. The significance of these results is related to the flexibility of the device: the same geometry provides qualitatively different transport properties in such a way that parameters are being varied in an experimentally achievable range.We calculate the spin transport properties of twodimensional rectangular arrays of nanoscale quantum rings, which can be fabricated from e.g. InAlAs/InGaAs based heterostructures [2] or HgTe/HgCdTe quantum wells [3], where Rashba-type [4] spin-orbit interaction (SOI) is present. This effect, which is essentially the same as the one which causes the fine structure in atomic spectra, results in spin precession for electrons moving in a semiconductor. It has already been demonstrated in experiments that the strength of this type of SOI can be controlled by external gate voltages [5,6] in the range of a few Volts. We propose devices in which the local manipulation of the SOI strength leads to effects which could be used in various practical spintronic applications. We focus on narrow rings in the ballistic (coherent) regime, where a one dimensional model provides appropriate description.The geometries we are considering (namely 3 × 3 and 5 × 5 ring arrays, see Fig. 1) have already appeared in a recent experiment [7] with rings of 100 nm thickness, and the case of uniform SOI strength has also been investigated theoretically [8,9]. We note that similarly to Ref. [7], the rings we consider here touch each other, thus the lines between them shown in the figures serve only visualization purposes. Considering wires of finite length would not p...