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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

On the measurability of the spin and magnetic moment of the free electron

Jørgen Kalckar

Published Apr 1, 1972• 5 citations
Publisher
DOI
10.1007/bf02722767

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In the late 1920s Niels Bohr propagated the idea that the magnetic moment of a free electron could not be observed. This derived from the idea that the spin degree of freedom characterized the electron only when it is bound in an atom. This view initiated a lively discussion, which involved many of the most prominent theoreticians of the time. The independent existence of the electron spin became an issue of principle. In particular it was deemed that quantum effects would destroy the separated classical trajectories in a Stern-- Gerlach type of experiment. We review these discussions and some later developments. Quantum effects do prove to be essential, but they do not overwhelm the magnetic effects of spin. In addition to these arguments, it has been possible experimentally to determine the electron g -factor with high accuracy in electromagnetic traps. In fact no principle seems to prevent the observation of the magnetic moment of the free electron.

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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.
In the late 1920s Niels Bohr propagated the idea that the magnetic moment of a free electron could not be observed. This derived from the idea that the spin degree of freedom characterized the electron only when it is bound in an atom. This view initiated a lively discussion, which involved many of the most prominent theoreticians of the time. The independent existence of the electron spin became an issue of principle. In particular it was deemed that quantum effects would destroy the separated classical trajectories in a Stern-- Gerlach type of experiment. We review these discussions and some later developments. Quantum effects do prove to be essential, but they do not overwhelm the magnetic effects of spin. In addition to these arguments, it has been possible experimentally to determine the electron g -factor with high accuracy in electromagnetic traps. In fact no principle seems to prevent the observation of the magnetic moment of the free electron.