Transverse Quantum Stern–Gerlach Magnets for Electrons

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