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Physical Review Letters

Method for Measuring the Cyclotron and Spin Resonance of Free Electrons

G. Gräff, F. G. Major, R. W. H. Roeder, Guenter Werth

Published Aug 5, 1968• 35 citations
Publisher

Abstract

The cyclotron and spin resonance of free electrons field confined in a small volume in ultrahigh vacuum have been observed via the rapid loss of electrons when their cyclotron motion is excited by the rf field and spin-dependent collision processes with polarized Na atoms in a beam, respectively. The electrons were polarized by spin exchange and then monitored through the spin dependence of the excitation process $e+\mathrm{Na}(3S)\ensuremath{\rightarrow}e+{\mathrm{Na}}^{*}(3P)$ and hence of their cooling rate.

DOI
10.1103/physrevlett.21.340

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The cyclotron and spin resonance of free electrons field confined in a small volume in ultrahigh vacuum have been observed via the rapid loss of electrons when their cyclotron motion is excited by the rf field and spin-dependent collision processes with polarized Na atoms in a beam, respectively. The electrons were polarized by spin exchange and then monitored through the spin dependence of the excitation process e+Na(3S)\ensuremath→e+Na∗(3P)e+\mathrm{Na}(3S)\ensuremath{\rightarrow}e+{\mathrm{Na}}^{*}(3P)e+Na(3S)\ensuremath→e+Na∗(3P) and hence of their cooling rate.
A single electron in a quantum cyclotron yields new measurements of the electron magnetic moment, given by g/2 = 1.00115965218073(28)[0.28 ppt], and the fine structure constant, α −1 = 137.035999084(51)[0.37 ppb], both significantly improved from prior results. The static magnetic and electric fields of a Penning trap confine the electron, and a 100 mK dilution refrigerator cools its cyclotron motion to the quantum-mechanical ground state. A quantum nondemolition measurement allows resolution of single cyclotron jumps and spin flips by coupling the cyclotron and spin energies to the frequency of the axial motion, which is self-excited and detected with a cryogenic amplifier. The trap electrodes form a high-Q microwave resonator near the cyclotron frequency; coupling between the cyclotron motion and cavity modes can inhibit spontaneous emission by over 100 timesthe free-space rate and shiftthe cyclotron frequency, a systematic effect that dominated the uncertainties of previous g-value measurements. A cylindrical trap geometry creates cavity modes with analytically calculable couplingsto cyclotron motion. Two independent methods use the cyclotron damping rate of an electron plasma or of the single electron itself as probes of the cavity mode structure and allow the identification ofthe modes by their geometries and couplings, the quantification of an offset between the mode and electrostatic centers, and the reduction of the cavity shift uncertainty to sub-dominant levels. Measuring g at four magnetic fields with cavity shifts spanning thirty times the final g-value uncertainty provides a check on the calculated cavity shifts. Magnetic field fluctuations limit the measurement of g by adding a noise-model dependence to the extraction of the cyclotron and anomaly frequencies from their resonance lines; the relative agreement of two line-splitting methods quantifies a lineshape model uncertainty. New techniques promise to increase field stability, narrow the resonance lines, and accelerate the measurement cycle. The measured g allows tests for physics beyond the Standard Model through searches for its temporal variation and comparisons with a “theoretical” g-value calculated from quantum electrodynamics and an independently measured fine structure constant.
A spin-exchange optical pumping experiment to study collisions between sodium atoms and free electrons is reported. In this experiment, electrons in a weak magnetic field were polarized by spin-exchange collisions with optically pumped sodium atoms. The sodium-electron collisions were the principal source of the electron resonance linewidth, and they also produced a shift in the electron resonance frequency. The magnitudes of the linewidth and the frequency shift depend upon the scattering amplitude for sodium-electron collisions, the sodium polarization, and the sodium atom density. The ratio of the frequency shift to the linewidth was 0.03. The sodium polarization was approximately 30%. The electron resonance frequency was lower when the sodium polarization was positive. The measurements of the electron linewidth and the frequency shift agree with theoretical values of the linewidth and frequency shift obtained from the sodium-electron scattering phase shifts which have been recently calculated by Garrett.
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The 3s-3p excitation of spin-polarized Na atoms by Ne+{\mathrm{Ne}}^{+}Ne+ ions has been studied for impact energies Elab=200{E}_{\mathrm{lab}=200}Elab=200​ eV to 6 keV, i.e., in the adiabatic regime. The total excitation cross section and the three Stokes polarization parameters of the fluorescence light have been measured. The linear polarization of the light shows a preferential excitation of the \ensuremath{\Vert}ml{m}_{l}ml​\ensuremath{\Vert}=1 magnetic substates. The circular polarization probes the spin orientation of the excited 3p state. At the highest impact energies investigated the experimental data are compatible with conservation of spin orientation during the collision. With decreasing impact energy, the spin polarization of the final 3p state becomes smaller than the spin polarization of the initial 3s state. This apparent spin depolarization is attributed to the exchange interaction between the Na valence electron and the unfilled Ne+{\mathrm{Ne}}^{+}Ne+ 2p5{p}^{5}p5 core in the quasimolecule formed during the collision.