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Physical Review Letters

Observation of the Continuous Stern-Gerlach Effect on an Electron Bound in an Atomic Ion

Nikolaus Hermanspahn, Hartmut Häffner, H. -Jürgen Kluge, W. Quint, S. Ståhl, J. Verdú, Günther Werth

Published Jan 17, 2000• 113 citations
Publisher

Abstract

We report on the first observation of the continuous Stern-Gerlach effect on an electron bound in an atomic ion. The measurement was performed on a single hydrogenlike ion ( 12C5+) in a Penning trap. The measured g factor of the bound electron, g = 2.001 042(2), is in excellent agreement with the theoretical value, confirming the relativistic correction at a level of 0.1%. This proves the possibility of g-factor determinations on atomic ions to high precision by using the continuous Stern-Gerlach effect. The result demonstrates the feasibility of conducting experiments on single heavy highly charged ions to test quantum electrodynamics in the strong electric field of the nucleus.

DOI
10.1103/physrevlett.84.427

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We report on the first observation of the continuous Stern-Gerlach effect on an electron bound in an atomic ion. The measurement was performed on a single hydrogenlike ion ( 12C5+) in a Penning trap. The measured g factor of the bound electron, g = 2.001 042(2), is in excellent agreement with the theoretical value, confirming the relativistic correction at a level of 0.1%. This proves the possibility of g-factor determinations on atomic ions to high precision by using the continuous Stern-Gerlach effect. The result demonstrates the feasibility of conducting experiments on single heavy highly charged ions to test quantum electrodynamics in the strong electric field of the nucleus.
We report on the measurement of the g-factor of the electron bound in an atomic ion. A single hydrogenic ion (12C5+) is stored in a Penning trap. The electronic spin state of the ion is monitored via the continuous Stern-Gerlach effect in a quantum non-demolition measurement. Quantum jumps between the two spin states (spin up and spin down) are induced by a microwave field at the spin precession frequency of the bound electron. The g-factor of the bound electron is obtained by varying the microwave frequency and counting the number of spin flips for a fixed time interval. Applications of the continuous Stern-Gerlach effect include high-accuracy tests of bound-state quantum electrodynamics (QED), the measurement of the atomic mass of the electron, the determination of the fine structure constant α, and the measurement of nuclear g-factors.
The measurement of the g -factor of the electron bound in a hydrogen-like ion is a high-accuracy test of the theory of quantum electrodynamics (QED) in strong fields. Here we report on the measurement of the g -factor of the bound electron in hydrogen-like oxygen ( 16 O 7+ ). In our experiment a single highly charged ion is stored in a Penning trap. The electronic spin state of the ion is monitored via the continuous Stern–Gerlach effect in a quantum non-demolition measurement. Quantum jumps between the two spin states (spin up and spin down ) are induced by a microwave field at the spin precession frequency of the bound electron. The g -factor of the bound electron is obtained by varying the microwave frequency and counting the number of spin flips. The comparison of our experimental values for the g -factor of the bound electron with the theoretical values shows excellent agreement and confirms the recent non-perturbative QED calculations.
In the relativistic description of atomic systems in external fields, the total momentum and the external electric field couple to the angular momentum of the individual particles. Therefore, the motional state of an ion in a particle trap influences measurements of internal observables such as energy levels or the ggg factor. We calculate the resulting relativistic shift of the Larmor frequency and the corresponding ggg-factor correction for a bound electron in a hydrogenlike ion in the 1S1 S1S state due to the ion moving in a Penning trap and show that it is negligible at the current precision of measurements. We also show that the analogous energy shift for measurements with an ion in the ground state of a Paul trap vanishes in leading order.
ALPHATRAP is a Penning-trap based experiment located at the Max-Planck-Institut für Kernphysik (MPIK). It is dedicated to the exploration of ground-state properties of heavy, highly charged ions (HCI). The major goal of the ALPHATRAP \nexperiment are high precision measurements of the bound-electron g-factor. The comparison of the experimental result with recent theoretical calculations will not only serve as a sensitive test of bound-state quantum electrodynamics (BS-QED) but also yields a new approach for the determination of fundamental constants such as the electron mass or the fine structure constant. The measurement of the bound-electron g-factor of a single HCI is performed in an optimized cryogenic double Penning-trap setup, utilizing the continuous Stern-Gerlach effect. For injection of externally produced HCI up to 208Pb81+ the ALPHATRAP experiment is \ncoupled to various ion sources, including the Heidelberg Electron-Beam Ion Trap. \nThis thesis describes the setup and preparation of the ALPHATRAP experiment on its way towards its first g-factor measurement. In this context a new highly sensitive detection system was implemented and successfully tested. This enabled a first commissioning of the whole apparatus with in situ generated HCI as well as HCI injected through the room temperature beamline. The first-time integration \nof an externally operable cryogenic valve allowed for excellent vacuum conditions with long ion storage times. The implementation of typical ion detection and manipulation techniques was demonstrated by characterization measurements of the detection system and the trapping fields. The commissioning culminated in the first direct observation of induced bound-electron spin transitions at the \nALPHATRAP experiment.
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.