Non-Uniform Magnetic Fields for Single-Electron Control

• URL: http://arxiv.org/abs/2311.06354v1
• Date: Fri, 10 Nov 2023 19:05:54 GMT
• Title: Non-Uniform Magnetic Fields for Single-Electron Control
• Authors: Mauro Ballicchia, Clemens Etl, Mihail Nedjalkov, Josef Weinbub
• Abstract summary: A gauge-invariant formulation of the Wigner equation for general electromagnetic fields has been proposed. We generalize this equation to include a general, non-uniform electric field and a linear, non-uniform magnetic field. This has led to explore a new type of transport inside electronic waveguides based on snake trajectories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Controlling single-electron states becomes increasingly important due to the wide-ranging advances in electron quantum optics. Single-electron control enables coherent manipulation of individual electrons and the ability to exploit the wave nature of electrons, which offers various opportunities for quantum information processing, sensing, and metrology. A unique opportunity offering new degrees of freedom for single-electron control is provided when considering non-uniform magnetic fields. Considering the modeling perspective, conventional electron quantum transport theories are commonly based on gauge-dependent electromagnetic potentials. A direct formulation in terms of intuitive electromagnetic fields is thus not possible. In an effort to rectify this, a gauge-invariant formulation of the Wigner equation for general electromagnetic fields has been proposed in [Nedjalkov et al., Phys. Rev. B., 2019, 99, 014423]. However, the complexity of this equation requires to derive a more convenient formulation for linear electromagnetic fields [Nedjalkov et al., Phys. Rev. A., 2022, 106, 052213]. This formulation directly includes the classical formulation of the Lorentz force and higher-order terms depending on the magnetic field gradient, that are negligible for small variations of the magnetic field. In this work, we generalize this equation in order to include a general, non-uniform electric field and a linear, non-uniform magnetic field. The thus obtained formulation has been applied to investigate the capabilities of a linear, non-uniform magnetic field to control single-electron states in terms of trajectory, interference patterns, and dispersion. This has led to explore a new type of transport inside electronic waveguides based on snake trajectories and also to explore the possibility to split wavepackets to realize edge states.

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