One electron was enough
In experiments at the University of Washington, Hans Dehmelt and his colleagues made one electron into a system they could keep and examine repeatedly. By the 1986 account of Van Dyck, Schwinberg and Dehmelt, a specially shaped Penning trap operated at four kelvin, only four degrees above absolute zero. Cooling reduced the electron’s motion while the fields kept it nearby.
The magnetic field bends its sideways motion into a circling path; shaped electric fields make it oscillate along the trap axis. A slower sideways drift completes the trapped motion. This uses steady fields, unlike Paul’s rapidly alternating electric trap. The electron remains in motion inside a small region, available for the next measurement.
Read the evidence: H. G. Dehmelt (1989), Experiments with an Isolated Subatomic Particle at Rest — Nobel lecture, geonium spectroscopy and Figs. 1–7R. S. Van Dyck, Jr., P. B. Schwinberg and H. G. Dehmelt (1986), Electron magnetic moment from geonium spectra: Early experiments and background concepts — author abstract, Phys. Rev. D 34, 722
Listen to the motion through the electrodes
An electron moving toward and away from an electrode changes the electrical charge induced on it. Connect the electrodes to a sensitive resonant circuit and that repeated motion can leave a radio-frequency signal. The instrument listens electrically to an oscillation too small to photograph.
Dehmelt’s lecture shows a way to count down to one electron: the signal changes in steps as electrons leave an initially small group. Once one remains, repeated observation can follow the same particle. Its oscillation frequency supplies the signal, but a further connection is needed to make that frequency reveal spin.
Read the evidence: H. G. Dehmelt (1989), Experiments with an Isolated Subatomic Particle at Rest — Nobel lecture, geonium spectroscopy and Figs. 1–7
Make the spin change the restoring force
Spin is an intrinsic quantum property that gives the electron a magnetic response. A magnetic field separates the energies of its two spin orientations. To read which one is occupied without ejecting the electron, the experiment adds a weak magnetic bottle: a field whose strength varies with position.
Moving along the trap axis now changes the electron’s magnetic energy. That adds a small contribution to the force restoring its axial motion. Reverse the spin and the contribution changes, shifting the oscillation frequency heard by the circuit. A spin flip becomes a step in an electrical frequency record.
This is the continuous Stern–Gerlach method. It retains the particle while monitoring a selected spin component. Cyclotron excitation, a change in the circling motion, also shifts the signal. The lecture distinguishes lasting baseline changes assigned to spin flips from shorter cyclotron excursions, using the preparation and the applied drives to identify what happened.
Read the evidence: H. G. Dehmelt (1989), Experiments with an Isolated Subatomic Particle at Rest — Nobel lecture, geonium spectroscopy and Figs. 1–7R. S. Van Dyck, Jr., P. B. Schwinberg and H. G. Dehmelt (1986), Electron magnetic moment from geonium spectra: Early experiments and background concepts — author abstract, Phys. Rev. D 34, 722
Compare two rhythms of the same electron
The spin resonance and the circling motion provide two frequencies in the same magnetic field. Their difference is called the anomaly frequency. Relative to the free cyclotron frequency, it reveals how far the electron’s spin factor departs from Dirac’s leading value of two. In the expression below, the anomaly and cyclotron frequencies are positive ordinary frequencies measured in the same units, and the spin factor is written as a positive magnitude.
The free cyclotron frequency means the circling rate without the confining electric field’s shift. The fast motion actually measured inside the trap must be corrected to recover it. Brown and Gabrielse showed how the observed trap-mode frequencies can be combined to suppress important effects of misalignment and electric-field imperfections. The comparison needs corresponding corrections to the measured anomaly frequency.
Read the evidence: L. S. Brown and G. Gabrielse (1982), Precision spectroscopy of a charged particle in an imperfect Penning trap — author abstract, Phys. Rev. A 25, 2423R. S. Van Dyck, Jr., P. B. Schwinberg and H. G. Dehmelt (1986), Electron magnetic moment from geonium spectra: Early experiments and background concepts — author abstract, Phys. Rev. D 34, 722
The trap became part of the precision measurement
A weak frequency shift is useful only when its spectral shape is understood. The magnetic bottle that makes spin visible also affects the resonance. Trap fields, particle motion and the detection procedure enter the analysis together. Van Dyck and colleagues’ 1986 account treated electric shifts and magnetic-bottle line shapes as part of extracting the magnetic moment.
Fan and colleagues’ separately dated 2023 measurement continued this approach with a different apparatus and much greater precision. The surrounding cavity changes both the electron’s radiative lifetime and its resonance frequency; those corrections still have to be evaluated. Keeping the same electron for repeated measurements makes such careful tests possible, turning a nearly isolated particle into its own small frequency laboratory.
Read the evidence: R. S. Van Dyck, Jr., P. B. Schwinberg and H. G. Dehmelt (1986), Electron magnetic moment from geonium spectra: Early experiments and background concepts — author abstract, Phys. Rev. D 34, 722X. Fan, T. G. Myers, B. A. D. Sukra and G. Gabrielse (2023), Measurement of the Electron Magnetic Moment, Phys. Rev. Lett. 130, 071801 — apparatus, frequency corrections and uncertainty budget