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

Proceedings of the National Academy of Sciences

Continuous Stern-Gerlach effect: Noise and the measurement process

HANS G. DEHMELT

Published May 1, 1986• 18 citations
Publisher

Abstract

This paper resumes the discussion of the continuous Stern-Gerlach effect, a method to continuously and nondestructively determine the spin state of the same individual electron, quasipermanently confined in a Penning trap in ultrahigh vacuum at liquid helium temperatures. Here the focus is on limitations to spin-state detection due to thermal and zero-point noise and on the quantum-mechanical measurement process. Illustrations of the continuous spin measurement process in the presence of selected perturbations are provided. The alteration of the spin state brought about by the frequency measurement process is exhibited. To resolve Zeno's paradox in a specific example, a slow resonant spin flip is discussed, when interrupted by frequent spin-state measurements. The continuous Stern-Gerlach effect is shown to be a near-ideal example for the quantum mechanical measurement process, for which all steps may be followed in quantitative detail.

DOI
10.1073/pnas.83.10.3074

Related papers

Continuous Stern-Gerlach effect: Principle and idealized apparatus (trapped single electron/aidal oscillation frequency/spin-dependent classical trajectories/reduction of wavefunction/measurement time)

HANS G. DEHMELT

A nondestructive type of Stern-Gerlach ef- fect for an individual electron is described that has been thoroughly demonstrated in experiments at the University of Washington. This Stern-Gerlach makes use of an inhomogeneous magnetic field provided by a weak auxiliary magnetic bottle and is nondestructive in contrast to all previous versions of the effect. As in the classic Stern-Gerlach effect, changes in the spin state are detected via changes in classical particle trajectories; however, what is observed now is not a deflection of the orbit but rather a change of its frequency in the storage well. A simplified model of the continuous Stern-Gerlach effect at zero temperature is introduced to develop the relation between minimum measurement time required for determination of spin state, driven oscillation amplitude, and zero-point fluctuations in the storage well. The problem of the reduction of the wavefunction by the interaction of the electron with the apparatus is addressed following W. Pauli.

•Jan 1, 2017•0 citations

Continuous Stern-Gerlach effect: Principle and idealized apparatus

HANS G. DEHMELT

A nondestructive type of Stern-Gerlach effect for an individual electron is described that has been thoroughly demonstrated in experiments at the University of Washington. This "continuous Stern-Gerlach effect" makes use of an inhomogeneous magnetic field provided by a weak auxiliary magnetic bottle and is nondestructive in contrast to all previous versions of the effect. As in the classic Stern-Gerlach effect, changes in the spin state are detected via changes in classical particle trajectories; however, what is observed now is not a deflection of the orbit but rather a change of its frequency in the storage well. A simplified model of the continuous Stern-Gerlach effect at zero temperature is introduced to develop the relation between minimum measurement time required for determination of spin state, driven oscillation amplitude, and zero-point fluctuations in the storage well. The problem of the reduction of the wavefunction by the interaction of the electron with the apparatus is addressed following W. Pauli.

Proceedings of the National Academy of Sciences•Apr 1, 1986•115 citations

The AC Stark, Stern-Gerlach, and Quantum Zeno Effects in Interferometric Qubit Readout

John A. Sidles

This article describes the AC Stark, Stern-Gerlach, and Quantum Zeno effects as they are manifested during continuous interferometric measurement of a two-state quantum system (qubit). A simple yet realistic model of the interferometric measurement process is presented, and solved to all orders of perturbation theory in the absence of thermal noise. The statistical properties of the interferometric Stern-Gerlach effect are described in terms of a Fokker-Plank equation, and a closed-form expression for the Green's function of this equation is obtained. Thermal noise is added in the form of a externally-applied Langevin force, and the combined effects of thermal noise and measurement are considered. Optical Bloch equations are obtained which describe the AC Stark and Quantum Zeno effects. Spontaneous qubit transitions are shown to be observationally equivalent to transitions induced by external Langevin forces. The effects of delayed choice are discussed. Practical experiments involving trapped ions are suggested. The results are relevant to the design of qubit readout systems in quantum computing, and to single-spin detection in magnetic resonance force microscopy.

arXiv:quant-ph/9612001•Nov 29, 1996•1 citation

Continuous Stern-Gerlach effect and the quantum-state diffusion model of state reduction

T. Steimle, G. Alber

A quantum-mechanical description of the continuous Stern-Gerlach effect is developed in which environmental effects, as well as effects arising from the continuous measurement of the electronic z motion, are taken into account. Master equations are presented that describe the behavior of a quantum statistical ensemble of continuous measurement processes. On the basis of these master equations and with the help of the quantum-state diffusion model a theoretical description of individual continuous measurement processes is developed. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Apr 1, 1996•8 citations

Stern-Gerlach Effect for Electron Beams

Herman Batelaan, T. J. Gay, J. J. Schwendiman

The conflict between Bohr's assertion that the magnetic moment of the electron cannot be measured with experiments based on the concept of classical trajectories, and the measurement of the magnetic moment of electrons in a modified Penning trap by Dehmelt et al. has led us to reevaluate other implications of Bohr's assertion. We show that, contrary to the analysis of Bohr and Pauli, the assumption of classical trajectories in a Stern-Gerlach--like device can result in a high degree of spin separation for an electron beam. This effect may persist within a fully quantum-mechanical analysis. The magnetic fields considered are such that a tabletop Stern-Gerlach electron spin filter is feasible.

Physical Review Letters•Dec 8, 1997•82 citations

Measurement of Ultralow Heating Rates of a Single Antiproton in a Cryogenic Penning Trap

M. J. Borchert, Pascal E. Blessing, J. A. Devlin +15 more

We report on the first detailed study of motional heating in a cryogenic Penning trap using a single antiproton. Employing the continuous Stern-Gerlach effect we observe cyclotron quantum transition rates of $6(1)\text{ }\text{ }\mathrm{quanta}/\mathrm{h}$ and an electric-field noise spectral density below $7.5(3.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }{\mathrm{V}}^{2}\text{ }{\mathrm{m}}^{\ensuremath{-}2}\text{ }{\mathrm{Hz}}^{\ensuremath{-}1}$, which corresponds to a scaled noise spectral density below $8.8(4.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }{\mathrm{V}}^{2}\text{ }{\mathrm{m}}^{\ensuremath{-}2}$, results which are more than 2 orders of magnitude smaller than those reported by other ion-trap experiments.

arXiv:1901.09860•Physical Review Letters•Jan 28, 2019•29 citations
This paper resumes the discussion of the continuous Stern-Gerlach effect, a method to continuously and nondestructively determine the spin state of the same individual electron, quasipermanently confined in a Penning trap in ultrahigh vacuum at liquid helium temperatures. Here the focus is on limitations to spin-state detection due to thermal and zero-point noise and on the quantum-mechanical measurement process. Illustrations of the continuous spin measurement process in the presence of selected perturbations are provided. The alteration of the spin state brought about by the frequency measurement process is exhibited. To resolve Zeno's paradox in a specific example, a slow resonant spin flip is discussed, when interrupted by frequent spin-state measurements. The continuous Stern-Gerlach effect is shown to be a near-ideal example for the quantum mechanical measurement process, for which all steps may be followed in quantitative detail.
A nondestructive type of Stern-Gerlach ef- fect for an individual electron is described that has been thoroughly demonstrated in experiments at the University of Washington. This Stern-Gerlach makes use of an inhomogeneous magnetic field provided by a weak auxiliary magnetic bottle and is nondestructive in contrast to all previous versions of the effect. As in the classic Stern-Gerlach effect, changes in the spin state are detected via changes in classical particle trajectories; however, what is observed now is not a deflection of the orbit but rather a change of its frequency in the storage well. A simplified model of the continuous Stern-Gerlach effect at zero temperature is introduced to develop the relation between minimum measurement time required for determination of spin state, driven oscillation amplitude, and zero-point fluctuations in the storage well. The problem of the reduction of the wavefunction by the interaction of the electron with the apparatus is addressed following W. Pauli.
A nondestructive type of Stern-Gerlach effect for an individual electron is described that has been thoroughly demonstrated in experiments at the University of Washington. This "continuous Stern-Gerlach effect" makes use of an inhomogeneous magnetic field provided by a weak auxiliary magnetic bottle and is nondestructive in contrast to all previous versions of the effect. As in the classic Stern-Gerlach effect, changes in the spin state are detected via changes in classical particle trajectories; however, what is observed now is not a deflection of the orbit but rather a change of its frequency in the storage well. A simplified model of the continuous Stern-Gerlach effect at zero temperature is introduced to develop the relation between minimum measurement time required for determination of spin state, driven oscillation amplitude, and zero-point fluctuations in the storage well. The problem of the reduction of the wavefunction by the interaction of the electron with the apparatus is addressed following W. Pauli.
This article describes the AC Stark, Stern-Gerlach, and Quantum Zeno effects as they are manifested during continuous interferometric measurement of a two-state quantum system (qubit). A simple yet realistic model of the interferometric measurement process is presented, and solved to all orders of perturbation theory in the absence of thermal noise. The statistical properties of the interferometric Stern-Gerlach effect are described in terms of a Fokker-Plank equation, and a closed-form expression for the Green's function of this equation is obtained. Thermal noise is added in the form of a externally-applied Langevin force, and the combined effects of thermal noise and measurement are considered. Optical Bloch equations are obtained which describe the AC Stark and Quantum Zeno effects. Spontaneous qubit transitions are shown to be observationally equivalent to transitions induced by external Langevin forces. The effects of delayed choice are discussed. Practical experiments involving trapped ions are suggested. The results are relevant to the design of qubit readout systems in quantum computing, and to single-spin detection in magnetic resonance force microscopy.
A quantum-mechanical description of the continuous Stern-Gerlach effect is developed in which environmental effects, as well as effects arising from the continuous measurement of the electronic z motion, are taken into account. Master equations are presented that describe the behavior of a quantum statistical ensemble of continuous measurement processes. On the basis of these master equations and with the help of the quantum-state diffusion model a theoretical description of individual continuous measurement processes is developed. \textcopyright{} 1996 The American Physical Society.
The conflict between Bohr's assertion that the magnetic moment of the electron cannot be measured with experiments based on the concept of classical trajectories, and the measurement of the magnetic moment of electrons in a modified Penning trap by Dehmelt et al. has led us to reevaluate other implications of Bohr's assertion. We show that, contrary to the analysis of Bohr and Pauli, the assumption of classical trajectories in a Stern-Gerlach--like device can result in a high degree of spin separation for an electron beam. This effect may persist within a fully quantum-mechanical analysis. The magnetic fields considered are such that a tabletop Stern-Gerlach electron spin filter is feasible.
We report on the first detailed study of motional heating in a cryogenic Penning trap using a single antiproton. Employing the continuous Stern-Gerlach effect we observe cyclotron quantum transition rates of 6(1)  quanta/h6(1)\text{ }\text{ }\mathrm{quanta}/\mathrm{h}6(1)  quanta/h and an electric-field noise spectral density below $7.5(3.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }{\mathrm{V}}^{2}\text{ }{\mathrm{m}}^{\ensuremath{-}2}\text{ }{\mathrm{Hz}}^{\ensuremath{-}1}$, which corresponds to a scaled noise spectral density below $8.8(4.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }{\mathrm{V}}^{2}\text{ }{\mathrm{m}}^{\ensuremath{-}2}$, results which are more than 2 orders of magnitude smaller than those reported by other ion-trap experiments.