In a quantum ring connected with two external leads the spin properties of an incoming electron are modified by the spin-orbit interaction resulting in a transformation of the qubit state carried by the spin. The ring acts as a one qubit spintronic quantum gate 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 size of the ring. We show that a large class of unitary transformations can be attained with already one ring -or a few rings in series -including the important cases of the Z, X, and Hadamard gates. By choosing appropriate parameters the spin transformations can be made unitary, which corresponds to lossless gates. The electron spin degree of freedom is one of the prospective carriers [1, 2] of qubits, the fundamental units in quantum information processing. In order to implement quantum operations on electron spins, appropriate gates are necessary that operate on this type of qubits. We note that in the present context the word 'gate' stands for an elementary logical operation [3]. In this paper we show that a one dimensional ring [4] connected with two external leads made of a semiconductor structure [5], such as InGaAs in which Rashba-type [6] spin-orbit interaction is the dominant spin-flipping mechanism, can render such a gate. Conductance properties of this kind of rings have been discussed earlier in the case of diametrically connected leads [7,8,9].By taking here a new point of view, we focus explicitly on the spin transformation characteristics of this device, and show that those can be appropriately controlled by varying its geometrical and physical parameters in the experimentally feasible range [7,8]. We shall determine the effects of changing the radius and the relative positions of the junctions, as well as the influence of varying the strength of the spin-orbit interaction via an external electric field. The conditions under which the incoming and transmitted spinors are connected unitarily will be determined, leading in principle, to a lossless single qubit gate. By connecting a few such rings in an appropriate manner, one can achieve practically all the important one qubit gates [3].We consider a ring of radius a in the x − y plane and assume a tunable static electric field [7] in the z direction characterized by the parameter α. Then the spin dependent Hamiltonian [9, 10] of a charged particle of effective mass m * iswhere ϕ is the azimuthal angle of a point on the ring, hΩ =h 2 /2m * a 2 is the parameter characterizing the kinetic energy of the charge and ω =α/ha is the frequency associated with the spin-orbit interaction. Apart from constants, the Hamiltonian (1) is the square of the sum of the z component of the orbital angular momentum operator L z = −i ∂ ∂ϕ , and of ω Ω S r , where S r = σ r /2 is the radial component of the spin (both measured in units ofh). H commutes in a nontrivial way with K = L z + S z , the z component of the total angular momentum. H also commutes...
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...
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