Wigner State Control for Entangled Electronics

The world of nanoelectronics is rich of yet unused quantum phenomena, promising novel device operation foundations as well as new computing approaches. The phrase Entangled Electronics is introduced, denoting a new branch of nanoelectronics, which unifies methods and principles for electron state control, aiming to create quantum states with certain desired properties. The underlying physics - featuring nanoscale dimensions involves quantum processes, which are highly-sensitive to the influence of the environment, called scattering. This project will develop theoretical, computational, and numerical approaches for enabling transient, multi-dimensional, and scattering-aware analysis of the highly complicated and not yet fully understood interplay between quantum and scattering phenomena for electron state control. We employ the Wigner formulation of quantum mechanics, as it offers the unique opportunity to treat both kinds of phenomena on equal footing. The proposed research relies on three major attainments of the successful precursor Austrian ScienceFund (FWF) project P21685-N22:Theoretical understanding of the role of physical scales on the electron behavior as well as of the existence of the Wigner solution, the signed-particle model for simulating Wigner dynamics, and prototypical implementations. The latter allowed to apply - for the first time - the Wigner approach to two- dimensional device potentials. This project will continue the successful research path and will particularly focus on the inclusion of the magnetic field, an interface to other existing approaches, applications for Entangled Electronics, and algorithmical aspects for enabling three-dimensional simulations. A systematic derivation of simulation models accounting for the magnetic field in the Wigner theory is still missing. A computationally feasible approach will be pursued, which allows for an efficient inclusion of magnetic processes in the Wigner signed-particle model. Electron transport in typical structures comprises phenomena with yet not explored physical and application aspects, thus giving rise to novel applications in the area of Entangled Electronics. The modelling and simulation approaches will require sophisticated computational methods, thus algorithmical advances will be made to enable three-dimensional simulations.

Entangled Electronics is a branch of nanoelectronics, which unifies methods and principles for electron state control, aiming to create quantum states with certain desired properties. The underlying physics - featuring nanoscale dimensions - involves superposition, interference and entanglement. These phenomena outline the research area of the project. Employed is the Wigner function formalism, which allows to treat both coherent and decoherence phenomena on equal footing. The work closely followed the research plan, summarized as follows. Incorporation of magnetic field into a numerically feasible Wigner particle model. A gauge invariant form of the Wigner equation, suitable for numerical analysis and corresponding to general electromagnetic conditions, has been derived. A relevant for a constant magnetic field and general electrostatic conditions particle model has been developed and applied to study magneto-tunneling. The obtained simulation results reveal the decoherence role of the magnetic field, which reduces the negativity of the Wigner function in the quantum regions of tunneling. The analysis shows that this effect is due to the local action of the magnetic field on the Wigner particles, which is velocity-dependent. Coupling of Wigner and NEGF formalisms. In a collaboration with the device modeling groups from University of Glasgow and ETH Zurich we developed a scheme, where the initial state of the electron is obtained by NEGF simulations and provides the initial condition for the Wigner particle model, which is used to simulate the further evolution of the electron. The joint work motivated the organization of the workshop 'Quantum Transport Methods and Algorithms: From Particles to Waves Approaches' Analysis of electron state control mechanisms. The processes of coherence systems and entan- glement have been investigated as promising for the manipulation of electron state evolution. Simulations show, that a double-dopant potential embedded in a quantum wire causes interfer- ence effects in the quantum state evolution, similarly to the fundamental double slit experiment demonstrating the wave nature of the electron. Logical devices based on such spatial resonance have been designed, which can implement all Boolean functions. Entanglement of two electrons is another process, fundamental for quantum information processing. However the problem is numerically hard for a quantum- statistical approach, because the variables double and the task becomes 8D even if a technologically modern two-dimensional (2D) material is considered. Development of efficient algorithms A self-consistent Wigner-Poisson coupling scheme for simu- lation of the process of Coulomb entanglement has been developed. The 8D task is reduced to two 4D coupled equations. Simulations of the evolution of the purity of the electrons during the process of entanglement demonstrate the feasibility of the approach.