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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

On the measurability of the spin of free electrons

Péter Faragó

Published Aug 1, 1972• 1 citation
Publisher
DOI
10.1007/bf02757120

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The cyclotron and spin resonance of free electrons field confined in a small volume in ultrahigh vacuum have been observed via the rapid loss of electrons when their cyclotron motion is excited by the rf field and spin-dependent collision processes with polarized Na atoms in a beam, respectively. The electrons were polarized by spin exchange and then monitored through the spin dependence of the excitation process $e+\mathrm{Na}(3S)\ensuremath{\rightarrow}e+{\mathrm{Na}}^{*}(3P)$ and hence of their cooling rate.
It is known that a quantum computer operating on electron-spin qubits with single-electron Hamiltonians and assisted by single-spin measurements can be simulated efficiently on a classical computer. We show that the exponential speedup of quantum algorithms is restored if single-charge measurements are added. These enable the construction of a CNOT (controlled NOT) gate for free fermions, using only beam splitters and spin rotations. The gate is nearly deterministic if the charge detector counts the number of electrons in a mode, and fully deterministic if it only measures the parity of that number.
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.