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arXiv:2602.15615

Magnetically assisted spin-resolved electron diffraction: Coherent control of spin population and spatial filtering

Sushanta Barman, Kuldeep Godara, Sudeep Bhattacharjee

quant-phSubmitted Feb 17, 2026• Announced Feb 18, 2026• Revised Mar 10, 2026 (v2)
v1 · Feb 17, 2026v2 · Mar 10, 2026
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Abstract

Electron diffraction from nanogratings provides a platform for free-electron interferometry, yet controlled manipulation of electron spin in such geometries remains largely unexplored. In particular, the role of the self-generated magnetic field arising from electron motion and the feasibility of coherent spin control without disrupting diffraction coherence have not been quantitatively investigated. In this article, a self-consistent Maxwell-Pauli framework is developed to study spin-resolved electron diffraction from nanogratings in the presence of magnetic fields. The model incorporates geometric confinement, image-charge interactions, self-generated magnetostatic fields, and externally applied magnetic fields. Numerical simulations show that the intrinsic magnetic self-field produced by the electron probability current is several orders of magnitude too weak to induce measurable spin mixing, demonstrating that nanogratings act as spin-conserving beam splitters under field-free conditions. When a uniform magnetic field is applied upstream of the nanograting, coherent Larmor precession enables controlled spin rotation without modifying the diffraction geometry or degrading coherence. The magnetic field required for a $π$ spin rotation scales inversely with the interaction length and electron de Broglie wavelength $λ_{dB}$. Furthermore, a downstream nonuniform magnetic field applied after the nanograting imparts a spatially varying Zeeman phase, producing opposite transverse momentum shifts for the two spin components. The spin-dependent transverse dynamics is analyzed using Husimi Q-function phase-space maps, which visualize spin-dependent population redistribution and momentum separation. The proposed approach enables tunable spatial separation of spin-resolved free electron beams and establishes an all-magnetic route for coherent spin rotation, control, and interferometry.

Comments
16 pages, 13 figures

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Electron diffraction from nanogratings provides a platform for free-electron interferometry, yet controlled manipulation of electron spin in such geometries remains largely unexplored. In particular, the role of the self-generated magnetic field arising from electron motion and the feasibility of coherent spin control without disrupting diffraction coherence have not been quantitatively investigated. In this article, a self-consistent Maxwell-Pauli framework is developed to study spin-resolved electron diffraction from nanogratings in the presence of magnetic fields. The model incorporates geometric confinement, image-charge interactions, self-generated magnetostatic fields, and externally applied magnetic fields. Numerical simulations show that the intrinsic magnetic self-field produced by the electron probability current is several orders of magnitude too weak to induce measurable spin mixing, demonstrating that nanogratings act as spin-conserving beam splitters under field-free conditions. When a uniform magnetic field is applied upstream of the nanograting, coherent Larmor precession enables controlled spin rotation without modifying the diffraction geometry or degrading coherence. The magnetic field required for a πππ spin rotation scales inversely with the interaction length and electron de Broglie wavelength λdBλ_{dB}λdB​. Furthermore, a downstream nonuniform magnetic field applied after the nanograting imparts a spatially varying Zeeman phase, producing opposite transverse momentum shifts for the two spin components. The spin-dependent transverse dynamics is analyzed using Husimi Q-function phase-space maps, which visualize spin-dependent population redistribution and momentum separation. The proposed approach enables tunable spatial separation of spin-resolved free electron beams and establishes an all-magnetic route for coherent spin rotation, control, and interferometry.
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We demonstrate complete coherent control of a single spin qubit confined in a self-assembled InAs negatively charged quantum dot subjected to an Oblique magnetic field, and directly compare this regime with the conventional Voigt geometry. In the Oblique-field configuration, the groundstate spin eigenstates are found to be unequal superpositions of the bare electron spin, with their composition tunable via the orientation of the applied field. This tunable spin mixing provides an additional degree of freedom to engineer the spin basis and associated optical couplings in the charged quantum dot system. Although this geometry has a distinct structure with important implications, it provides a regime in which we can fully and coherently control the tailored spin qubit. We observe Rabi oscillations and Ramsey fringes, and demonstrate arbitrary single-qubit rotations, enabling a direct comparison with the Voigt case. Our results establish that spin-qubit control does not necessarily require a pure Voigt geometry and can instead be achieved under Oblique magnetic fields. This relaxes constraints on device and field alignment and offers a versatile route to design and optimize quantum information processing architectures in semiconductor quantum dots.
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Electron matter waves coherently diffract when passing through a periodic structure of light formed by two interfering light waves. In this so-called Kapitza-Dirac effect, the electron momentum changes due to absorption and emission of photons via stimulated Compton scattering. Until now, the effect has only been observed with low energy electrons due to the small momentum of a visible photon compared to the momentum of high energy electron leading to diffraction angles of 10^(-4) rad or smaller. We report on the observation of the Kapitza-Dirac effect in a scanning electron microscope using high energy (20 and 30 keV) electrons with de-Broglie wavelengths of 9 pm and 7 pm, respectively. The photon sidebands in the electron transverse momentum spectrum are detected in the convergent beam diffraction geometry using spatial filtering. As the coupling strength between the electrons and the light field increases, the sideband populations exhibit coherent, reversible oscillations among diffraction orders. The effect can serve as a coherent electron beam-splitter or a phase-plate in various types of electron microscopes.
The coherent control of carrier spin states in semiconductor quantum dots (QDs) is a key requirement for certain quantum information applications, particularly where lightmatter interactions are involved such as in the generation of spin-photon entangled states. A widely used approach for spin control involves Larmor precession in an externally applied magnetic field. Increasing the magnetic field strength enhances the spin precession rate, thus improving the photon generation rate. However, this also introduces Zeeman splitting, which lifts the spin-state degeneracy. As a result frequency distinguishability is introduced, reducing the fidelity of the entangled spinphoton states. This work explores a novel approach to mitigate the Zeeman splitting by employing the AC Stark effect via a red-detuned laser. The Stark shift counteracts the Zeeman energy difference, effectively restoring transition degeneracy within the transition linewidth while allowing for an increased magnetic field strength and consequently a faster precession rate. Theoretical modelling demonstrates that this technique enables an almost doubling of the current spin precession frequency while maintaining nearly degenerate optical transitions. To validate this approach, a high-precision optical system is under development to probe QD emission under simultaneous magnetic and optical fields. Simulations incorporating both effects confirm the feasibility of this method for eliminating frequency distinguishability. These results lay the groundwork for the development of scalable quantum dot-based photonic platforms for quantum communication and information processing.
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