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AIP conference proceedings

The g-factor of the bound electron in hydrogenic ions

W. Quint

Published Jan 1, 2001• 1 citation
Publisher

Abstract

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.

DOI
10.1063/1.1354354

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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.
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.
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.
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.