Two-electron selective coupling in an edge-state based conditional phase shifter

Abstract

We investigate the effect of long-range Coulomb interaction on the two-electron scattering in the integer quantum Hall regime at bulk filling factor two. We compute the dynamics of the exact two-particle wave function by means of a parallel version of the split-step Fourier method in a 2D potential background reproducing the effect of depleting gates in a realistic heterostructure, with the charge carrier represented by a localized wave packet of edge states. We compare the spatial shift induced by Coulomb repulsion in the final two-electron wave function for two indistinguishable electrons initialized in different configurations according to their Landau index and analyze their bunching probability and the effect of screening. We finally prove the feasibility of this device as a two-qubit conditional phase shifter able to generate controlled entanglement from product states.

Coherent spin transport through helical edge states of topological insulator

“…Similar to the low-temperature case [34][35][36][37][38] , one can suggest twoqubit manipulation schemes taking into account the electron-electron interaction. To this end, one can use interferometers connected in parallel and coupled by interaction (see Fig.…”

“…The transmission coefficient and the spin polarization are expressed in terms of the matrixt as follows (38) where 〈…〉 ϵ stands for thermal averaging. Here, we neglect the Rashba coupling and assume that the incoming electrons are unpolarized.…”

“…Such qubits can be controlled by changing the magnetic field and the strength of the SO interaction 17,33 . Taking into account, the electron-electron interaction makes it also possible to construct effective two-qubit computational schemes in two coupled interferometers based on conventional materials 35,36 , on edge states of the integer quantum Hall effect 37,38 and on helical states 34 . Signatures of electron-electron interaction in HES was already observed experimentally 39,40 .…”

Time-dependent transport in Graphene Mach-Zender Interferometers

“…We simulate the full two-dimensional system in real space, in order to capture the behaviour of the wave packet in the most realistic and immediate way. Our group has previously performed various studies for MZIs in GaAs/AlGaAs heterostructures, where the dynamics of the propagating carriers is limited to the conduction band [50][51][52][53][54]. Here we include the whole band structure in the proximity of the valleys in the Brillouin Zone, and consider the electronic wave function as a four-component spinor.…”

Gate-Controlled Electron Quantum Interference Logic

“…Key enabling technologies are: electron sources (e.g., electron dynamics in a silicon source 4 , two-electron sources 5 , gate-tunable quantum dot in MoS 2 6 ), coherent circuits 7 , and electron detection 8 . All these technologies are key to electronic quantum applications in sensing 9 , metrology 10 , tomography 11 , and information processing (i.e., flying charge qubit systems 1,12,13 ). As is shown in this work, electron quantum optics also provides particular exciting opportunities for a novel type of quantum interference structure.…”