Abstract
In the Stern–Gerlach experiment, silver atoms were separated according to their spin state (Gerlach and Stern 1922 Z. Phys. 9 353–355). This experiment demonstrates the quantization of spin and relies on the classical description of motion. However, so far, no design has led to a functional Stern–Gerlach magnet for free electrons. Bohr and Pauli showed in the 1930 Solvay conference that Stern–Gerlach magnets for electrons cannot work, at least if the design is based on classical trajectories (Pauli W 1932 Proc. of the 6th Solvay Conf. 2 (1930) (Brussels: Gauthier-Villars) pp 183–86, 217–20, 275–80; Pauli W 1964 Collected Scientific Papers ed R Kronig and V F Weiskopf, vol 2 (New York: Wiley)). Here, we present ideas for the realization of a Stern–Gerlach magnet for electrons in which spin and motion are treated fully quantum mechanically. We show that a magnetic phase grating composed of a regular array of microscopic current loops can separate electron diffraction peaks according to their spin states. The experimental feasibility of a diffractive approach is compared to that of an interferometric approach. We show that an interferometric arrangement with magnetic phase control is the functional equivalent of an electron Stern–Gerlach magnet.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. In 1930, Bohr and Pauli showed that the complete spatial separation of the spin states of free electrons is impossible if the experiment is based on the concept of classical trajectories. This statement has since been interpreted as meaning that a functional Stern–Gerlach magnet for electrons is impossible. Recently, it has been shown, using a fully quantum mechanical analysis, that the spin states of an electron can, in principle, be fully separated in a direction parallel to their initial velocity. A more practical transverse spin splitting, as in the original Stern–Gerlach experiment, has not yet been conceived.
Main results. The possibility of fully separating the spin states of a free electron beam in a direction perpendicular to the initial velocity is shown. We show that an interferometric arrangement with magnetic phase control is the functional equivalent of an electron Stern–Gerlach magnet, and is experimentally feasible.
Wider implications. The interferometric approach to the transverse Stern–Gerlach magnet for electrons could result in an alternative polarized electron source. Also, the Stern–Gerlach effect is one of the cornerstones of quantum mechanics and is of fundamental and historic importance. The results of this paper add a deeper understanding of this effect as it pertains to electrons, and contribute to a discussion that involves amongst others Bohr, Pauli and Dehmelt.