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Laser Physics

A Microscopic Stern-Gerlach Magnet for Electrons?

Daniel L. Freimund, Herman Batelaan

Published Jan 1, 2003• 5 citations
OpenAlex

Abstract

We discuss the possibility of realizing a microscopic Stern--Gerlach magnet for electrons using counter-propagating bichromatic laser light. Absorption of two photons with frequency 0) combined with stimulated emission of one photon with frequency 2ω allows for the conservation of energy, momentum, and angular momentum, The possibility of constructing such a device appears to be an open question,

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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.

New Journal of Physics•Jun 28, 2011•24 citations

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Stern-Gerlach effect of weak-light ultraslow vector solitons

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We propose a scheme to exhibit Stern-Gerlach deflection of high-dimensional vector optical solitons at a weak-light level in a cold atomic gas via electromagnetically induced transparency. We show that the propagating velocity and generation power of such solitons can be reduced to ${10}^{\ensuremath{-}6}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}c$ ($c$ is light speed in vacuum) and lowered to magnitude of nanowatt, respectively. The stabilization of the solitons is realized by using an optical lattice potential formed by a far-detuned laser field, and trajectories of them are deflected significantly by using a transversal Stern-Gerlach gradient magnetic field. Deflection angles of the solitons can be of magnitude of ${10}^{\ensuremath{-}3}$ rad when propagating several millimeters. Different from atomic Stern-Gerlach deflection, deflection angles of the solitons can be distinct for different polarization components and can be manipulated in a controllable way. The result obtained can be described in terms of the Stern-Gerlach effect for vector optical solitons with quasispin and effective magnetic moment.

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Observing the spin of free electrons in action(Stern-Gerlach experiment by free electrons)

Hosein Majlesi

Stern-Gerlach experiment by free electron is very important experiment because it answered some questions that remain unanswered for almost a century. Bohr and Pauli considered its objective observation as impossible while some other scientists considered such observation as possible. The experiment on free electrons has not been conducted so far because the high magnetic field gradient predicted there was thought as impossible to generate. This paper proves that it is not only possible but also observable using a high vacuum lamp which is deionized well. To obtain a high magnetic field gradient, it is not necessary to have a very strong magnetic field and it is possible to observe the phenomenon using a very sharp pointed magnet and adjusting the voltage in a certain distance from free electron beams. that objective observation requires your consideration of some technical points simultaneously.In this experiment, no electric field and no magnetic field does not change with time.

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Exact theory of the Stern-Gerlach experiment - extended version

G. Coddens

The Stern-Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin-up or spin-down. But that theory is based on mathematical errors in the way it (mis)treats spinors and group theory.We present here a mathematically rigorous theory for a fermion in a magnetic field, which is no longer counter-intuitive. It is based on an understanding of spinors in SU(2) which is only Euclidean geometry.Contrary to what Pauli has been reading into the Stern-Gerlach experiment,the spin directions are not quantized. The new corrected paradigm, which solves all conceptual problems, is that the fermions precess around the magnetic-field just as Einstein and Ehrenfest had conjectured.Surprizingly this leads to only two energy states, which should be qualified as precession-up and precession-down rather thanspin-up and spin down.Indeed, despite the presence of the many different possible angles $\theta$ betweenthe spin axis ${\mathbf{s}}$ and the magnetic field ${\mathbf{B}}$, the fermions can only have two possible energies $m_{0}c^{2}\pm\mu B$. The values $\pm\mu B$ do thus not correspond to the continuum of values $-{\boldsymbol{\mu\cdot}}{\mathbf{B}}$ Einstein and Ehrenfest had conjectured. The energy term $V= -{\boldsymbol{\mu\cdot}}{\mathbf{B}}$ is a macroscopic quantity. It is a statistical average over a large ensemble of fermions distributed over the two microscopic states with energies $\pm\mu B$, and as such not valid for individual fermions. The two fermion states with energy $\pm\mu B$ are not potential-energy states. We also explain themathematically rigorous meaning of the up and down spinors. They represent left-handed and right-handed reference frames, such that now everything is intuitively clearand understandable in simple geometrical terms. The paradigm shift does not affect the Pauli principle.

•Dec 11, 2020•0 citations

Coherent regime of Kapitza-Dirac effect with electrons

Kamila Moriová, Petr Koutenský, Neli Laštovičková Streshkova +5 more

Electron matter waves coherently diffract when passing through a periodic structure of light formed by two interfering light waves. In this so-called Kapitza-Dirac effect, the electron momentum changes due to absorption and emission of photons via stimulated Compton scattering. Until now, the effect has only been observed with low energy electrons due to the small momentum of a visible photon compared to the momentum of high energy electron leading to diffraction angles of 10^(-4) rad or smaller. We report on the observation of the Kapitza-Dirac effect in a scanning electron microscope using high energy (20 and 30 keV) electrons with de-Broglie wavelengths of 9 pm and 7 pm, respectively. The photon sidebands in the electron transverse momentum spectrum are detected in the convergent beam diffraction geometry using spatial filtering. As the coupling strength between the electrons and the light field increases, the sideband populations exhibit coherent, reversible oscillations among diffraction orders. The effect can serve as a coherent electron beam-splitter or a phase-plate in various types of electron microscopes.

quant-pharXiv:2511.14508•Physical Review Letters•Nov 19, 2025•0 citations
We discuss the possibility of realizing a microscopic Stern--Gerlach magnet for electrons using counter-propagating bichromatic laser light. Absorption of two photons with frequency 0) combined with stimulated emission of one photon with frequency 2ω allows for the conservation of energy, momentum, and angular momentum, The possibility of constructing such a device appears to be an open question,
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.
We propose a scheme to exhibit Stern-Gerlach deflection of high-dimensional vector optical solitons at a weak-light level in a cold atomic gas via electromagnetically induced transparency. We show that the propagating velocity and generation power of such solitons can be reduced to ${10}^{\ensuremath{-}6}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}c$ (ccc is light speed in vacuum) and lowered to magnitude of nanowatt, respectively. The stabilization of the solitons is realized by using an optical lattice potential formed by a far-detuned laser field, and trajectories of them are deflected significantly by using a transversal Stern-Gerlach gradient magnetic field. Deflection angles of the solitons can be of magnitude of ${10}^{\ensuremath{-}3}$ rad when propagating several millimeters. Different from atomic Stern-Gerlach deflection, deflection angles of the solitons can be distinct for different polarization components and can be manipulated in a controllable way. The result obtained can be described in terms of the Stern-Gerlach effect for vector optical solitons with quasispin and effective magnetic moment.
Stern-Gerlach experiment by free electron is very important experiment because it answered some questions that remain unanswered for almost a century. Bohr and Pauli considered its objective observation as impossible while some other scientists considered such observation as possible. The experiment on free electrons has not been conducted so far because the high magnetic field gradient predicted there was thought as impossible to generate. This paper proves that it is not only possible but also observable using a high vacuum lamp which is deionized well. To obtain a high magnetic field gradient, it is not necessary to have a very strong magnetic field and it is possible to observe the phenomenon using a very sharp pointed magnet and adjusting the voltage in a certain distance from free electron beams. that objective observation requires your consideration of some technical points simultaneously.In this experiment, no electric field and no magnetic field does not change with time.
The Stern-Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin-up or spin-down. But that theory is based on mathematical errors in the way it (mis)treats spinors and group theory.We present here a mathematically rigorous theory for a fermion in a magnetic field, which is no longer counter-intuitive. It is based on an understanding of spinors in SU(2) which is only Euclidean geometry.Contrary to what Pauli has been reading into the Stern-Gerlach experiment,the spin directions are not quantized. The new corrected paradigm, which solves all conceptual problems, is that the fermions precess around the magnetic-field just as Einstein and Ehrenfest had conjectured.Surprizingly this leads to only two energy states, which should be qualified as precession-up and precession-down rather thanspin-up and spin down.Indeed, despite the presence of the many different possible angles θ\thetaθ betweenthe spin axis s{\mathbf{s}}s and the magnetic field B{\mathbf{B}}B, the fermions can only have two possible energies m0c2±μBm_{0}c^{2}\pm\mu Bm0​c2±μB. The values ±μB\pm\mu B±μB do thus not correspond to the continuum of values −μ⋅B-{\boldsymbol{\mu\cdot}}{\mathbf{B}}−μ⋅B Einstein and Ehrenfest had conjectured. The energy term V=−μ⋅BV= -{\boldsymbol{\mu\cdot}}{\mathbf{B}}V=−μ⋅B is a macroscopic quantity. It is a statistical average over a large ensemble of fermions distributed over the two microscopic states with energies ±μB\pm\mu B±μB, and as such not valid for individual fermions. The two fermion states with energy ±μB\pm\mu B±μB are not potential-energy states. We also explain themathematically rigorous meaning of the up and down spinors. They represent left-handed and right-handed reference frames, such that now everything is intuitively clearand understandable in simple geometrical terms. The paradigm shift does not affect the Pauli principle.
Electron matter waves coherently diffract when passing through a periodic structure of light formed by two interfering light waves. In this so-called Kapitza-Dirac effect, the electron momentum changes due to absorption and emission of photons via stimulated Compton scattering. Until now, the effect has only been observed with low energy electrons due to the small momentum of a visible photon compared to the momentum of high energy electron leading to diffraction angles of 10^(-4) rad or smaller. We report on the observation of the Kapitza-Dirac effect in a scanning electron microscope using high energy (20 and 30 keV) electrons with de-Broglie wavelengths of 9 pm and 7 pm, respectively. The photon sidebands in the electron transverse momentum spectrum are detected in the convergent beam diffraction geometry using spatial filtering. As the coupling strength between the electrons and the light field increases, the sideband populations exhibit coherent, reversible oscillations among diffraction orders. The effect can serve as a coherent electron beam-splitter or a phase-plate in various types of electron microscopes.