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Optical and Quantum Sensing and Precision Metrology II

Numerical modeling of the multi-stage Stern–Gerlach experiment by Frisch and Segrè using co-quantum dynamics via the Schrödinger equation

Zhe He, Kelvin Titimbo, David C. Garrett, S. Suleyman Kahraman, Lihong V. Wang

Published Mar 12, 2024• 0 citations
Publisher

Abstract

The 1922 experiment of Stern and Gerlach that initially provided evidence of the quantization of the angular momentum is now a prototypical example of quantum measurement. Frisch and Segrè in 1932 extended the experiment to include two Stern–Gerlach apparatuses separated by an inner rotation chamber, in which a varying magnetic field produces partial electron spin flipping. To this day, quantum mechanical treatments inadequately predict the experimental observations. Here, we use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern–Gerlach experiment conducted by Frisch and Segrè. Our simulation solves the Schrödinger equation with electron-nuclear interactions according to CQD and utilizes a branching condition (extended Pauli exclusion principle) postulated by CQD to predict the collapse of electron spins; the outcome agrees with the measurements of the fraction of spin flipping and supports CQD as a potential model for electron spin evolution and collapse.

DOI
10.1117/12.3002106

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The 1922 experiment of Stern and Gerlach that initially provided evidence of the quantization of the angular momentum is now a prototypical example of quantum measurement. Frisch and Segrè in 1932 extended the experiment to include two Stern–Gerlach apparatuses separated by an inner rotation chamber, in which a varying magnetic field produces partial electron spin flipping. To this day, quantum mechanical treatments inadequately predict the experimental observations. Here, we use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern–Gerlach experiment conducted by Frisch and Segrè. Our simulation solves the Schrödinger equation with electron-nuclear interactions according to CQD and utilizes a branching condition (extended Pauli exclusion principle) postulated by CQD to predict the collapse of electron spins; the outcome agrees with the measurements of the fraction of spin flipping and supports CQD as a potential model for electron spin evolution and collapse.
Abstract We use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern–Gerlach (SG) experiment conducted by R. Frisch and E. Segrè. This experiment consists of two SG apparatuses separated by an inner rotation chamber that varies the fraction of spin flip. To this day, quantum mechanical treatments inadequately predict the Frisch–Segrè experiment. Here, we account for electron-nuclear interactions according to CQD and solve the associated Schrödinger equation. Our simulation utilizes a branching condition to predict the collapse of electron spins, and the outcome agrees with the Frisch–Segrè experimental observation and supports CQD as a potential model for electron spin evolution and collapse.
We use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern$\unicode{x2013}$Gerlach (SG) experiment conducted by R. Frisch and E. Segrè. This experiment consists of two Stern$\unicode{x2013}$Gerlach apparatuses separated by an inner rotation chamber that varies the fraction of spin flip. To this day, quantum mechanical treatments inadequately predict the Frisch$\unicode{x2013}$Segrè experiment. Here, we account for electron-nuclear interactions according to CQD and solve the associated Schrödinger equation. Our simulation outcome agrees with the Frisch$\unicode{x2013}$Segrè experimental observation and supports CQD as a potential model for electron spin evolution and collapse.
The Stern–Gerlach experiment stands as one of the fundamental demonstrations of quantum phenomena. A successive combination of Stern–Gerlach apparatuses was first explored as a gedankenexperiment by Heisenberg to study angular momentum quantization further; later a detailed experiment was proposed by Einstein to Stern and Ehrenfest. Here, we numerically study the spin flip in the Frisch–Segrè experiment, the first successful multi-stage Stern–Gerlach experiment, within the context of the novel co-quantum dynamics theory. Despite early attempts by P. Güttinger, E. Majorana, I.I. Rabi, L. Landau, C. Zener, and E. Stückelberg among others, theoretical descriptions deviate from the Frisch and Segrè observations. We model the middle stage responsible for spin rotation by sampling the atoms with the Monte Carlo method and solving the dynamics of the electron and nuclear magnetic moments numerically according to the Bloch equation. The simulated dynamics shows that co-quantum dynamics closely reproduces, without using any fitting parameters, the experimental observations reported by Frisch and Segrè in 1933, which have so far lacked theoretical predictions using the standard theories.
Abstract We numerically study the spin flip in the Frisch–Segrè experiment, the first multi-stage Stern–Gerlach experiment, within the context of the novel co-quantum dynamics (CQD) theory. We model the middle stage responsible for spin rotation by sampling the atoms with the Monte Carlo method and solving the dynamics of the electron and nuclear magnetic moments numerically according to the Bloch equation. The simulation shows that CQD closely reproduces, without using any fitting parameters, the experimental observations reported by Frisch and Segrè in 1933, which have so far lacked theoretical predictions.
We numerically study the spin flip in the Frisch$\unicode{x2013}$Segrè experiment, the first multi-stage Stern$\unicode{x2013}$Gerlach experiment, within the context of the novel co-quantum dynamics theory. We model the middle stage responsible for spin rotation by sampling the atoms with the Monte Carlo method and solving the dynamics of the electron and nuclear magnetic moments numerically according to the Bloch equation. Our results show that, without using any fitting parameters, the co-quantum dynamics closely reproduces the experimental observation reported by Frisch and Segrè in 1933, which has so far lacked theoretical predictions.
The multi-stage Stern–Gerlach experiment conducted by Frisch and Segrè has been modeled analytically using quantum mechanics by Majorana and revised by Rabi by including the hyperfine interaction. However, the closed-form analytical predictions, which rely on approximations, do not match the experimental observation well. To avoid the approximations, we numerically solve the standard quantum mechanical model, via the von Neumann equation, which includes the hyperfine interaction for the time evolution of the spin. The outcome is compared with the experimental observation and the predictions by Majorana, Rabi, and an alternative model called co-quantum dynamics. Thus far, the coefficients of determination from the standard quantum mechanical model, which does not use free parameters, are still below zero. Non-standard variants that improve the match are explored.