Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Observation of the transverse Stern-Gerlach effect in neutral potassium and an analysis of a charged particle Stern-Gerlach experiment

Eric Enga

Published Jan 1, 2011• 0 citations
Publisher

Abstract

Two experiments are described. One is the successful observation of the resonant deflection of a beam of neutral potassium atoms at a frequency of 7.2 Mhz, in agreement with the predictions of the theory of the Transverse Stern-Gerlach (TGS) experiment. The other is a proposal for a charged particle Stern-Gerlach experiment, which is based on an extension of the TSG experiment to time independent, inhomogeneous magnetic fields having the form [formula omitted] If the field B₁(r) is well chosen, the charged particle trajectories are confined in a stable beam by the resulting Lorentz forces for motion generally along the z axis. This is, in fact, the principle of strong focusing which is now widely used in accelerator design. But in such a system it is also possible to satisfy the criterion for a TSG experiment, since in a frame of reference moving with a particle in the z direction, the field B₁(r) is rotating in time.

DOI
10.14288/1.0084805

Related papers

OBSERVATION OF THE TRANSVERSE STERN–GERLACH EFFECT IN NEUTRAL POTASSIUM

Myer Bloom, Eric Enga, Hin Lew

A successful transverse Stern–Gerlach experiment has been performed, using a beam of neutral potassium atoms and an inhomogeneous time-dependent magnetic field of the form[Formula: see text]A classical analysis of the Stern–Gerlach experiment is given for a rotating inhomogeneous magnetic field. In general, when space quantization is achieved, the spins are quantized along the effective magnetic field in the reference frame rotating with angular velocity ω about the z axis. For ω = 0, the direction of quantization is the z axis (conventional Stern–Gerlach experiment), while at resonance (ω = −γH 0 ) the direction of quantization is the x axis in the rotating reference frame (transverse Stern–Gerlach experiment). The experiment, which was performed at 7.2 Mc, is described in detail.

Canadian Journal of Physics•Apr 1, 1967•26 citations

A charged particle Stern–Gerlach experiment

Eric Enga, Myer Bloom

It is shown that a charged particle Stern–Gerlach experiment can be performed in a magnetic field geometry which is similar to that used in accelerators of the strong-focusing type. In particular, we analyze the helical quadrupole system. The analysis is based on an extension of the theory of the transverse Stern–Gerlach experiment to time-independent, inhomogeneous magnetic fields. The effect of the Lorentz force is reduced by using orthogonal inhomogeneous electric fields.

Canadian Journal of Physics•Nov 1, 1970•4 citations

Critical Examination of a Proposed Charged-Particle Stern–Gerlach Experiment

Thomas F. Knott

It has been proposed by Enga and Bloom that combined electric and magnetic helical quadrupole fields may be used to perform a Stern–Gerlach experiment on charged particles. A detailed investigation shows that the longitudinal Lorentz force due to coupling of the transverse velocity of the particles to the transverse magnetic field produces an additional focusing effect which masks the Stern–Gerlach force in large regions of initial phase space. Consideration of uncompensated magnetic fields, produced by small random variations in conductor dimensions and location, shows that the tolerances required to preserve spin separation in the useful range of initial conditions are several orders of magnitude higher than can be achieved at this time.

Canadian Journal of Physics•Feb 1, 1972•1 citation

Stern–Gerlach splitting of low-energy ion beams

Carsten Henkel, Georg Jacob, Felix Stopp +4 more

Abstract We present a feasibility study with several magnetic field configurations for creating spin-dependent forces that can split a low-energy ion beam by the Stern–Gerlach (SG) effect. To the best of our knowledge, coherent spin-splittings of charged particles have yet to be realised. Our proposal is based on ion source parameters taken from a recent experiment that demonstrated single-ion implantation from a high-brightness ion source combined with a radio-frequency Paul trap. The inhomogeneous magnetic fields can be created by permanently magnetised microstructures or from current-carrying wires with sizes in the micron range, such as those recently used in a successful implementation of the SG effect with neutral atoms. All relevant forces (Lorentz force and image charges) are taken into account, and measurable splittings are found by analytical and numerical calculations.

arXiv:1903.04061•New Journal of Physics•Jul 30, 2019•11 citations

A Numerical Experiment with the Stern-Gerlach Geometry

Riadh Al Rabeh

The Stern-Gerlach (SG) experiment reported in 1922 was an important milestone in the history of physics. The passing of a collimated neutral beam of silver atoms through a long, strong and asymmetrical magnet caused the atoms of silver out of a horizontal slit to split roughly into two separate beams forming a hollow lip figure (as seen on a plate held normal to the beam) instead of being a filled-in lip figure as suggested by some theoretical calculations. The SG results were thought to indicate that the observed phenomenon can not be explained using classical physics. Following a classical numerical approach by the author using a double-slit geometry, results are given for a 3D numerical SG type experiment showing clearly that a binary beam splitting is possible for certain conditions using an inverse square relation as the only source of forces- thus giving the possibility of a classical interpretation to the problem. For simplicity, we use what is mathematically equivalent- a dipole of charges to represent the magnetic dipole of the atom, and sets of fixed charges or potential surfaces around the path of the beam to represent the poles of a magnet. Although not exactly following the SG setup, the present results, nonetheless, are useful in showing the clear discrete behavior that can be caused by the combination of a fixed boundary, a strong field asymmetry and the highly nonlinear mapping of the inverse square law of forces coupled with the spin direction of a particle.

•Jan 1, 2011•0 citations

Direct demonstration of the transverse Stern–Gerlach effect

J. L. Porter, R. F. Pettifer, David R Leadley

A Stern–Gerlach experiment constructed in the spirit of the original experiment is reported that demonstrates spatial quantization for a beam of silver atoms directly to the unaided eye. Splitting of the atomic beam is seen both parallel to the magnetic field direction, as in the “usual” experiment, and in a direction mutually perpendicular to the field and atomic trajectory, which is a new transverse Stern–Gerlach effect. Splitting of up to 4 mm can be recorded visually. Calculations based on the force components acting on the atomic beams reproduce the experimental results within the experimental accuracy of ±0.3 mm.

American Journal of Physics•Oct 13, 2003•3 citations
Two experiments are described. One is the successful observation of the resonant deflection of a beam of neutral potassium atoms at a frequency of 7.2 Mhz, in agreement with the predictions of the theory of the Transverse Stern-Gerlach (TGS) experiment. The other is a proposal for a charged particle Stern-Gerlach experiment, which is based on an extension of the TSG experiment to time independent, inhomogeneous magnetic fields having the form [formula omitted] If the field B₁(r) is well chosen, the charged particle trajectories are confined in a stable beam by the resulting Lorentz forces for motion generally along the z axis. This is, in fact, the principle of strong focusing which is now widely used in accelerator design. But in such a system it is also possible to satisfy the criterion for a TSG experiment, since in a frame of reference moving with a particle in the z direction, the field B₁(r) is rotating in time.
A successful transverse Stern–Gerlach experiment has been performed, using a beam of neutral potassium atoms and an inhomogeneous time-dependent magnetic field of the form[Formula: see text]A classical analysis of the Stern–Gerlach experiment is given for a rotating inhomogeneous magnetic field. In general, when space quantization is achieved, the spins are quantized along the effective magnetic field in the reference frame rotating with angular velocity ω about the z axis. For ω = 0, the direction of quantization is the z axis (conventional Stern–Gerlach experiment), while at resonance (ω = −γH 0 ) the direction of quantization is the x axis in the rotating reference frame (transverse Stern–Gerlach experiment). The experiment, which was performed at 7.2 Mc, is described in detail.
It has been proposed by Enga and Bloom that combined electric and magnetic helical quadrupole fields may be used to perform a Stern–Gerlach experiment on charged particles. A detailed investigation shows that the longitudinal Lorentz force due to coupling of the transverse velocity of the particles to the transverse magnetic field produces an additional focusing effect which masks the Stern–Gerlach force in large regions of initial phase space. Consideration of uncompensated magnetic fields, produced by small random variations in conductor dimensions and location, shows that the tolerances required to preserve spin separation in the useful range of initial conditions are several orders of magnitude higher than can be achieved at this time.
Abstract We present a feasibility study with several magnetic field configurations for creating spin-dependent forces that can split a low-energy ion beam by the Stern–Gerlach (SG) effect. To the best of our knowledge, coherent spin-splittings of charged particles have yet to be realised. Our proposal is based on ion source parameters taken from a recent experiment that demonstrated single-ion implantation from a high-brightness ion source combined with a radio-frequency Paul trap. The inhomogeneous magnetic fields can be created by permanently magnetised microstructures or from current-carrying wires with sizes in the micron range, such as those recently used in a successful implementation of the SG effect with neutral atoms. All relevant forces (Lorentz force and image charges) are taken into account, and measurable splittings are found by analytical and numerical calculations.
The Stern-Gerlach (SG) experiment reported in 1922 was an important milestone in the history of physics. The passing of a collimated neutral beam of silver atoms through a long, strong and asymmetrical magnet caused the atoms of silver out of a horizontal slit to split roughly into two separate beams forming a hollow lip figure (as seen on a plate held normal to the beam) instead of being a filled-in lip figure as suggested by some theoretical calculations. The SG results were thought to indicate that the observed phenomenon can not be explained using classical physics. Following a classical numerical approach by the author using a double-slit geometry, results are given for a 3D numerical SG type experiment showing clearly that a binary beam splitting is possible for certain conditions using an inverse square relation as the only source of forces- thus giving the possibility of a classical interpretation to the problem. For simplicity, we use what is mathematically equivalent- a dipole of charges to represent the magnetic dipole of the atom, and sets of fixed charges or potential surfaces around the path of the beam to represent the poles of a magnet. Although not exactly following the SG setup, the present results, nonetheless, are useful in showing the clear discrete behavior that can be caused by the combination of a fixed boundary, a strong field asymmetry and the highly nonlinear mapping of the inverse square law of forces coupled with the spin direction of a particle.
A Stern–Gerlach experiment constructed in the spirit of the original experiment is reported that demonstrates spatial quantization for a beam of silver atoms directly to the unaided eye. Splitting of the atomic beam is seen both parallel to the magnetic field direction, as in the “usual” experiment, and in a direction mutually perpendicular to the field and atomic trajectory, which is a new transverse Stern–Gerlach effect. Splitting of up to 4 mm can be recorded visually. Calculations based on the force components acting on the atomic beams reproduce the experimental results within the experimental accuracy of ±0.3 mm.