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Technobius physics.

Investigation of splitting of a beam of potassium atoms in the classical Stern-Gerlach experiment at varying inhomogeneity of the magnetic field

Asel' Akhmetova

Published Dec 29, 2024• 0 citations
Publisher

Abstract

The splitting of a beam of potassium atoms in the classical Stern-Gerlach scheme under varying inhomogeneity of the magnetic field is experimentally investigated in this work. First, the basic shape of the beam in the absence of an effective field is recorded, which makes it possible to introduce and calibrate the geometrical parameters of the channel. Then, when the current in the magnet windings increases and the field gradient grows, a systematic shift of the beam density maxima is observed, described by the model function F(u), which includes the parameter q, which characterizes the strength of interaction of atoms with the field. Theoretical calculations based on this function showed good agreement with the experimental results, including the asymmetry of the distribution due to the nonideal symmetry of the magnetic system. The obtained dependences of the position of the intensity maxima on ∇B confirmed the validity of both linear and asymptotic approximation for different modes of magnet operation. These conclusions have both fundamental importance for understanding the quantum mechanical aspects of beam splitting and applied significance in the development of methods for precise control of spin-polarized atomic beams in spectroscopy and spintronics.

DOI
10.54355/tbusphys/2.4.2024.0024

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The splitting of a beam of potassium atoms in the classical Stern-Gerlach scheme under varying inhomogeneity of the magnetic field is experimentally investigated in this work. First, the basic shape of the beam in the absence of an effective field is recorded, which makes it possible to introduce and calibrate the geometrical parameters of the channel. Then, when the current in the magnet windings increases and the field gradient grows, a systematic shift of the beam density maxima is observed, described by the model function F(u), which includes the parameter q, which characterizes the strength of interaction of atoms with the field. Theoretical calculations based on this function showed good agreement with the experimental results, including the asymmetry of the distribution due to the nonideal symmetry of the magnetic system. The obtained dependences of the position of the intensity maxima on ∇B confirmed the validity of both linear and asymptotic approximation for different modes of magnet operation. These conclusions have both fundamental importance for understanding the quantum mechanical aspects of beam splitting and applied significance in the development of methods for precise control of spin-polarized atomic beams in spectroscopy and spintronics.
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.
An atom interferometer using two Stern-Gerlach magnets as polariser and analyser is described. The interferometer was first operated with a thermal beam of ground state potassium atoms. In that case the beam splitters are two radio-frequency zones within a transverse homogeneous magnetic field building a coherent superposition of Zeeman states. Ramsey fringes are obtained by scanning the RF-frequency through the resonance profile. Pulsing the RF power allows to get the time-of-flight distribution of the beam. Atomic interference fringes (``Stern-Gerlach fringes'') are observed when the magnitude of an inhomogeneous magnetic field located in between the beam splitters is scanned. When the inhomogeneous field is also pulsed, the scalar Bohm-Aharonov effect is observed. The use of metastable helium atoms (He*23S) in place of potassium atoms is proposed. In addition to the usual advantages provided by metastable atoms of high internal energy, this atom offers the specific advantage to behave as an ideal spin-one particle. This allows us to greatly simplify the polarisation scheme of the interferometer. Possible applications involving transversally inhomogeneous magnetic fields are given and limitations due to the finite source size and angular aperture are discussed.
We report the observation of the splitting of an atomic beam by the optical Stern-Gerlach effect. A beam of metastable He atoms interacts with a nearly or exactly resonant laser field with a well-defined intensity gradient perpendicular to the atomic beam. The coherent splitting of the atomic beam is produced in the case of exact resonance. For the nonresonant case, a deflection of the atomic beam is observed. We have studied the splitting and deflection of the atomic beam as a function of laser detuning from resonance. Our results are in good agreement with theoretical predictions.
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.
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.
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.