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arXiv:2602.20852

Simulating Microwave-Controlled Spin Imaging with Free-Space Electrons

Santiago Beltrán-Romero, Stefan Löffler, Dennis Rätzel, Philipp Haslinger

quant-phSubmitted Feb 24, 2026• Announced Feb 25, 2026
arXivHTMLPDF

Abstract

Coherent spin resonance techniques, such as nuclear and electron spin resonance spectroscopy, have revolutionized non-invasive imaging by providing spectrally resolved information about spin dynamics. Motivated by the recent emergence of electron microscopy methods capable of sensing microwave-excitations, we establish a theoretical framework for Spin Resonance Spectroscopy (SRS) in transmission electron microscopy (TEM). This technique combines microwave pump fields with focused electron probe beams to enable state-selective spin imaging at the atomic scale. Using scattering theory, we model the interaction between free-space electrons and electron spin systems, capturing both elastic and inelastic processes. The strongest effect of the spin system on the free electron is a magnetic phase shift. Our simulations demonstrate that phase shifts from individual electron spins are detectable in both image mode and diffraction mode. In principle, differential measurements under microwave control allow the extraction of local resonance frequencies that are influenced by the surrounding spin environment. By evaluating the Classical Fisher Information (CFI), we identify imaging conditions that maximize the signal-to-noise ratio (SNR), showing how defocus and beam width affect the measurement sensitivity. These findings establish a foundation for integrating SRS with high-resolution TEM, bridging spin spectroscopy and atomic-scale imaging, and enabling new capabilities in quantum spin research and nanoscale materials characterization.

Comments
12 pages, 3 figures

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Abstract Recent advances in transmission electron microscopy (TEM) have opened the path toward spin resonance spectroscopy with single-spin sensitivity. To assess this potential, we investigate the quantum precision limits for sensing magnetic moments with free-electron probes. Using a scattering model where an electron wavepacket interacts with a localized spin, we study two metrological tasks: estimating the magnitude of the magnetic moment and discriminating the presence of a spin. The sensitivity for a given measurement setting is generally determined by the classical Fisher information, which we benchmark against the quantum bound optimized over all measurements. We find that conventional TEM imaging can saturate the quantum bound when backaction of the probe electron onto the spin state is negligible. We also find that, when backaction is relevant, one could do better by realizing a measurement of the electron's orbital angular momentum state. These results establish the quantum limits of spin sensing in TEM and guide the development of future experiments probing individual electron spins or nanoscale ensembles of nuclear spins.
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We provide a theoretical framework to describe the dynamics of a free-electron beam interacting with quantized bound systems in arbitrary electromagnetic environments. This expands the quantum optics toolbox to incorporate free-electron beams for applications in highly tunable quantum control, imaging, and spectroscopy at the nanoscale. The framework recovers previously studied results and shows that electromagnetic environments can amplify the intrinsically weak coupling between a free-electron and a bound electron to reach previously inaccessible interaction regimes. We leverage this enhanced coupling for experimentally feasible protocols in coherent qubit control and towards the nondestructive readout and projective control of the electron beam's quantum-number statistics. Our framework is broadly applicable to microwave-frequency qubits, optical nanophotonics, cavity quantum electrodynamics, and emerging platforms at the interface of electron microscopy and quantum information.