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Bulletin of the American Physical Society

Electron Matter Optics and the Quantum Electron Stern-Gerlach Magnet

Scot McGregor, Roger Bach, Xiaolu Yin, S. H. Liou, Herman Batelaan, Glen Gronniger

Published Jun 16, 2011• 0 citations
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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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Abstract The Stern–Gerlach (SG) effect provided the first direct experimental evidence of the quantization of electron spin. Although some analog SG effects have been proposed in optical systems, finding a perfect optical analog for the SG effect remains a challenge. Here, a novel optical SG effect is demonstrated in periodically poled electro‐optical crystals. Induced by an applied electric field, the principal axes of crystal rock periodically along the propagation direction of light. When the quasi‐phase‐matching condition is satisfied, the electro‐optical coupling process within the periodically poled crystal can be accurately described by the Schrödinger–Pauli equation for spin‐1/2 particles. The output photons can be deflected toward opposite directions according to their intrinsic spin angular momentum (circular polarizations), since the transversely varying duty cycle of crystal arises an effective magnetic‐field gradient. Moreover, the output photons can be separated according to two arbitrary orthogonal polarization states, allowing us to construct high‐speed electro‐optically tunable polarization beam splitters for arbitrary orthogonal polarization states. Therefore, the optical SG effect provides not only a perfect optical analog for the quantum SG effect but also a useful optical element for optics and quantum physics.

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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.
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.
Abstract The Stern–Gerlach (SG) effect provided the first direct experimental evidence of the quantization of electron spin. Although some analog SG effects have been proposed in optical systems, finding a perfect optical analog for the SG effect remains a challenge. Here, a novel optical SG effect is demonstrated in periodically poled electro‐optical crystals. Induced by an applied electric field, the principal axes of crystal rock periodically along the propagation direction of light. When the quasi‐phase‐matching condition is satisfied, the electro‐optical coupling process within the periodically poled crystal can be accurately described by the Schrödinger–Pauli equation for spin‐1/2 particles. The output photons can be deflected toward opposite directions according to their intrinsic spin angular momentum (circular polarizations), since the transversely varying duty cycle of crystal arises an effective magnetic‐field gradient. Moreover, the output photons can be separated according to two arbitrary orthogonal polarization states, allowing us to construct high‐speed electro‐optically tunable polarization beam splitters for arbitrary orthogonal polarization states. Therefore, the optical SG effect provides not only a perfect optical analog for the quantum SG effect but also a useful optical element for optics and quantum physics.