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

Physical Review A

Consideration of possible mass and velocity corrections to magnetic cluster experiments

Z.Y. Liu, P. A. Dowben, Alexey Popov, David P. Pappas

Published Mar 12, 2003• 3 citations
Publisher

Abstract

Gadolinium occurs, in natural abundance, as several isotopes. The possible combinations of different gadolinium isotopes dictates that even for a fixed number of atoms in the cluster, clusters of gadolinium atoms will exhibit a range of masses. This and the expected consequence of the translation energy distributions are explored as possible corrections to Stern-Gerlach cluster beam-deflection experiments. Upon closer inspection of the experimental data, we find that the translation energy plus the vibrational temperature distribution may be inhomogeneous. This could be the origin of a long tail to high deflections in the experimental deflection profiles, at low cluster temperatures, in the magnetic cluster Stern-Gerlach experiments.

DOI
10.1103/physreva.67.033202

Related papers

Stern-Gerlach Deflection of Metallic-Cluster Beams

Walter D. Knight, R. Monot, Eberhard Dietz +1 more

Supersonic argon beams containing clusters of from 1 to 100 potassium atoms show magnetic deflection patterns with three components: atoms, undeflectable clusters comprising mainly even numbers of atoms, and clusters with odd numbers of atoms. The magnetic moments of the light odd clusters are approximately 1${\mathrm{\ensuremath{\mu}}}_{\mathrm{B}}$.

Physical Review Letters•May 15, 1978•50 citations

Double Stern-Gerlach experiments on Mn@Sn12 : Refocusing of a paramagnetic superatom

Thomas M. Fuchs, Rolf Schäfer

We report magnetic double deflection experiments on cryogenically cooled $\mathrm{Mn}@{\mathrm{Sn}}_{12}$ clusters. Refocusing efficiencies of up to 90% are achieved by keeping the magnetic-flux density virtually constant between the two Stern-Gerlach magnets. The spin dynamics are probed by introducing magnetic-flux density variations along the molecular-beam path. We apply a microscopic model for the interpretation of our results taking the coupling of electronic spin and rotational degrees of freedom into account. The combination of our experimental and theoretical results reveals unexpected insights into the interplay between rotation and spin dynamics of small metal clusters depending on magnetic-field modulations.

Physical Review A•Dec 11, 2018•21 citations

Theory of relaxation of magnetic clusters in a Stern-Gerlach setup

Sushanta Dattagupta, S. D. Mahanti

We use a stochastic theory approach to discuss different scenarios such as ``locked moment'' and ``superparamagnetic'' behavior of magnetic clusters seen in Stern-Gerlach (SG) experiments. A dimensionless parameter $\ensuremath{\lambda}{\ensuremath{\tau}}_{E}$ (where \ensuremath{\lambda} is an internal spin relaxation rate and ${\ensuremath{\tau}}_{E}$ is the time spent by the cluster in the field gradient region) and the initial polarization of the cluster moment are shown to determine sensitively the position of the cluster beam on the SG screen.

Physical review. B, Condensed matter•May 1, 1998•1 citation

Polarisation measurement of a He(23Si1) atomic beam

J Giroux, Robby Lapointe, R.J. Slobodrian

An atomic beam of He in the metastable 2 3 S 1 state can be atomic-spin-polarised by Stern-Gerlach selection using a sextupole magnet. The authors report the first measurements of the polarisation obtained by this method. The authors have determined the metastable beam velocity distribution from a time-of-flight measurement. The distribution was found to be in the range of thermal velocities. The selection efficiency of the sextupole magnet was studied using a Stern-Gerlach deflection with an inhomogeneous dipole field. The experimental results give a vector polarisation close to 95%. Thus, the technique can be useful for many applications.

Journal of Physics E Scientific Instruments•Nov 1, 1984•1 citation

Simulation of atom trajectories in the original Stern–Gerlach experiment

Faraz Mostafaeipour, S. Suleyman Kahraman, Kelvin Titimbo +2 more

Abstract Following a comprehensive analysis of the historical literature, we model the geometry of the Stern–Gerlach experiment to numerically calculate the magnetic field using the finite-element method. Using this calculated field and Monte Carlo methods, the semiclassical atomic translational dynamics are simulated to produce the well-known quantized end-pattern with matching dimensions. The finite-element method used provides the most accurate description of the Stern–Gerlach magnetic field and end-pattern in the literature, matching the historically reported values and figures.

arXiv:2408.14530•Physica Scripta•Mar 11, 2025•1 citation

A Century Ago the Stern–Gerlach Experiment Ruled Unequivocally in Favor of Quantum Mechanics

Břetislav Friedrich

Abstract In 1921, Otto Stern conceived the idea for an experiment that would decide between a classical and a quantum description of atomic behavior, as epitomized by the Bohr–Sommerfeld–Debye model of the atom. This model entailed not only the quantization of the magnitude of the orbital electronic angular momentum but also of the projection of the angular momentum on an external magnetic field – the so‐called space quantization. Stern recognized that space quantization would have observable consequences: namely, that the magnetic dipole moment due to the orbital angular momentum would be space quantized as well, taking two opposite values for atoms whose only unpaired electron has just one quantum of orbital angular momentum. When acted upon by a suitable inhomogeneous magnetic field, a beam of such atoms would be split into two beams consisting of deflected atoms with opposite projections of the orbital angular momentum on the magnetic field. In contradistinction, if atoms behaved classically, the atomic beam would only broaden along the field gradient and have maximum intensity at zero deflection, i. e., where there would be a minimum or no intensity for a beam split due to space quantization. Stern anticipated that, although simple in principle, the experiment would be difficult to carry out – and invited Walther Gerlach to team up with him. Gerlach's realism and experimental skills together with his sometimes stubborn determination to make things work proved invaluable for the success of the Stern–Gerlach experiment (SGE). After a long struggle, Gerlach finally saw, on 8 February 1922, the splitting of a beam of silver atoms in a magnetic field. The absence of the concept of electron spin confused and confounded the interpretation of the SGE, as the silver atoms were, in fact, in a 2S state, with zero orbital and spin angular momentum. However, a key quantum feature whose existence the SGE was designed to test – namely space quantization of electronic angular momentum – was robust enough to transpire independent of whether the electronic angular momentum was orbital or due to spin. The SGE entails other key aspects of quantum mechanics such as quantum measurement, state preparation, coherence, and entanglement. Confronted with the outcome of the SGE, Stern noted: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.”

Israel Journal of Chemistry•Jun 28, 2023•6 citations
Gadolinium occurs, in natural abundance, as several isotopes. The possible combinations of different gadolinium isotopes dictates that even for a fixed number of atoms in the cluster, clusters of gadolinium atoms will exhibit a range of masses. This and the expected consequence of the translation energy distributions are explored as possible corrections to Stern-Gerlach cluster beam-deflection experiments. Upon closer inspection of the experimental data, we find that the translation energy plus the vibrational temperature distribution may be inhomogeneous. This could be the origin of a long tail to high deflections in the experimental deflection profiles, at low cluster temperatures, in the magnetic cluster Stern-Gerlach experiments.
We report magnetic double deflection experiments on cryogenically cooled Mn@Sn12\mathrm{Mn}@{\mathrm{Sn}}_{12}Mn@Sn12​ clusters. Refocusing efficiencies of up to 90% are achieved by keeping the magnetic-flux density virtually constant between the two Stern-Gerlach magnets. The spin dynamics are probed by introducing magnetic-flux density variations along the molecular-beam path. We apply a microscopic model for the interpretation of our results taking the coupling of electronic spin and rotational degrees of freedom into account. The combination of our experimental and theoretical results reveals unexpected insights into the interplay between rotation and spin dynamics of small metal clusters depending on magnetic-field modulations.
We use a stochastic theory approach to discuss different scenarios such as ``locked moment'' and ``superparamagnetic'' behavior of magnetic clusters seen in Stern-Gerlach (SG) experiments. A dimensionless parameter $\ensuremath{\lambda}{\ensuremath{\tau}}_{E}$ (where \ensuremath{\lambda} is an internal spin relaxation rate and ${\ensuremath{\tau}}_{E}$ is the time spent by the cluster in the field gradient region) and the initial polarization of the cluster moment are shown to determine sensitively the position of the cluster beam on the SG screen.
An atomic beam of He in the metastable 2 3 S 1 state can be atomic-spin-polarised by Stern-Gerlach selection using a sextupole magnet. The authors report the first measurements of the polarisation obtained by this method. The authors have determined the metastable beam velocity distribution from a time-of-flight measurement. The distribution was found to be in the range of thermal velocities. The selection efficiency of the sextupole magnet was studied using a Stern-Gerlach deflection with an inhomogeneous dipole field. The experimental results give a vector polarisation close to 95%. Thus, the technique can be useful for many applications.
Abstract Following a comprehensive analysis of the historical literature, we model the geometry of the Stern–Gerlach experiment to numerically calculate the magnetic field using the finite-element method. Using this calculated field and Monte Carlo methods, the semiclassical atomic translational dynamics are simulated to produce the well-known quantized end-pattern with matching dimensions. The finite-element method used provides the most accurate description of the Stern–Gerlach magnetic field and end-pattern in the literature, matching the historically reported values and figures.
Abstract In 1921, Otto Stern conceived the idea for an experiment that would decide between a classical and a quantum description of atomic behavior, as epitomized by the Bohr–Sommerfeld–Debye model of the atom. This model entailed not only the quantization of the magnitude of the orbital electronic angular momentum but also of the projection of the angular momentum on an external magnetic field – the so‐called space quantization. Stern recognized that space quantization would have observable consequences: namely, that the magnetic dipole moment due to the orbital angular momentum would be space quantized as well, taking two opposite values for atoms whose only unpaired electron has just one quantum of orbital angular momentum. When acted upon by a suitable inhomogeneous magnetic field, a beam of such atoms would be split into two beams consisting of deflected atoms with opposite projections of the orbital angular momentum on the magnetic field. In contradistinction, if atoms behaved classically, the atomic beam would only broaden along the field gradient and have maximum intensity at zero deflection, i. e., where there would be a minimum or no intensity for a beam split due to space quantization. Stern anticipated that, although simple in principle, the experiment would be difficult to carry out – and invited Walther Gerlach to team up with him. Gerlach's realism and experimental skills together with his sometimes stubborn determination to make things work proved invaluable for the success of the Stern–Gerlach experiment (SGE). After a long struggle, Gerlach finally saw, on 8 February 1922, the splitting of a beam of silver atoms in a magnetic field. The absence of the concept of electron spin confused and confounded the interpretation of the SGE, as the silver atoms were, in fact, in a 2S state, with zero orbital and spin angular momentum. However, a key quantum feature whose existence the SGE was designed to test – namely space quantization of electronic angular momentum – was robust enough to transpire independent of whether the electronic angular momentum was orbital or due to spin. The SGE entails other key aspects of quantum mechanics such as quantum measurement, state preparation, coherence, and entanglement. Confronted with the outcome of the SGE, Stern noted: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.”