Double quantum ring with Rashba spin-orbit interaction as a quantum NOT gate

During the last years, many studies have been done on mesoscopic quantum rings made of semiconductors like InGaAs because of their ability to show quantum interference effects such as Aharonov-Bohm oscillations and spin dependent quantum transport (spintronics). The study of electronics and spintronics in mesoscopic systems can be used to improve designing and manufacturing of quantum computing devices. Manipulating spin degree of freedom is one of important fundamental subjects in quantum computing field. One of mechanisms which can control spin transport of electron is Rashba spin-orbit interaction. In previous works spin-polarized persistent current, spin-filtered electron transmission to single quantum ring and also spin separation via a three terminal quantum ring have been proposed using Rashba spin-orbit interaction. In this study we introduce double quantum rings connected each other by a normal lead with perpendicular electric field implied on each of them. Electron beam injected from an incoming lead which is connected to the first quantum ring and transmitted to an outgoing lead connected to the second quantum ring. We use S-matrix formalism to study spin dependent transport of electron through this system. We find that by adjusting parameters of the system (such as the Rashba spin-orbit interaction, geometry of connected rings, strength of coupling constant of leads to the rings and energy of the incident electron beam) properly the system can act as a quantum NOT gate which flips the spin of injected electron from up to down and vice versa.