Electron spin separation in a simple Stern-Gerlach field

L. C. García de Andrade, C. Sivaran

Herman Batelaan, T. J. Gay, J. J. Schwendiman

The conflict between Bohr's assertion that the magnetic moment of the electron cannot be measured with experiments based on the concept of classical trajectories, and the measurement of the magnetic moment of electrons in a modified Penning trap by Dehmelt et al. has led us to reevaluate other implications of Bohr's assertion. We show that, contrary to the analysis of Bohr and Pauli, the assumption of classical trajectories in a Stern-Gerlach--like device can result in a high degree of spin separation for an electron beam. This effect may persist within a fully quantum-mechanical analysis. The magnetic fields considered are such that a tabletop Stern-Gerlach electron spin filter is feasible.

Scot McGregor, Roger Bach, Herman Batelaan

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.

L. C. García de Andrade

Jiaxin Li, Zhaoyuan Wang, Yi Hu +1 more

Abstract Stern‐Gerlach (SG) effect, initially found for unveiling the existence of quantized electron spins, is now a general concept describing a state‐dependent separation. It is widely explored in optics to achieve a function of optical splitting, but the current schemes always require a polarization‐ or wavelength‐dependent process, thus showing limitations for broader applications. Here, spatial modes of an optical field are employed as another degree of freedom to demonstrate an SG effect. Two modes of a pair of coupled waveguides are found to be in analog to the electron spins. They are able to undergo a splitting upon a spatially‐dependent waveguide coupling, which plays the role of a non‐uniform magnetic field. In an experiment, such a splitting is realized in two coupled non‐parallel slab waveguides, and its strength is adjusted at ease by varying the parameters of this proposed structure. This SG‐related optical splitting may find applications in the field of optical sensing and signal processing.