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Bulletin of the American Physical Society

Eliminating cavity shifts from electron magnetic moment (g-2) measurements

G. Gabrielse

Published May 1, 1993• 0 citations
OpenAlex

Abstract

A cylindrical Penning trap is of such high quality that a single electron is observed with good signal-to-noise. The trap is also a good approximation to an ideal cylindrical microwave cavity. This is documented in situ at 4 K with a new probe utilizing trapped electrons. An extraordinary control of the cavity-electron interaction results and opens the way to a new generation of electron magnetic moment measurements, not limited by either cavity frequency shifts or damping widths, and to sideband cooling of an electron motion to very low (mK) temperatures.

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Physical Review A•Oct 1, 1987•13 citations
A cylindrical Penning trap is of such high quality that a single electron is observed with good signal-to-noise. The trap is also a good approximation to an ideal cylindrical microwave cavity. This is documented in situ at 4 K with a new probe utilizing trapped electrons. An extraordinary control of the cavity-electron interaction results and opens the way to a new generation of electron magnetic moment measurements, not limited by either cavity frequency shifts or damping widths, and to sideband cooling of an electron motion to very low (mK) temperatures.
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.
With a superposition of static electric and magnetic fields, a Penning trap can confine a single electron indefinitely. A weak coupling of the electron to its environment makes the system ideal for precision measurements but renders detection of the electron’s motion difficult. In order to measure fundamental properties of an electron, we employ a Penning trap cooled by a dilution refrigerator. This experimental setup requires extremely low-noise and low-power cryogenic amplifiers for detection of the electron’s axial motion. We design and demonstrate new amplifiers, resulting in a significant decrease of the axial temperature and in an improved signal to noise ratio. We use feedback to cool the axial motion and to self-excite the axial motion for continuous monitoring of the axial frequency. These techniques for cooling and measuring the axial frequency may contribute to an improved measurement of the electron g factor, a more stringent CPT test in leptons, and a more precise measurement of the proton-electron mass ratio.
Electronic feedback is used to self-excite the axial oscillation of a single electron in a Penning trap. Large, stable, easily detected oscillations arise even in an anharmonic potential. Amplitudes are controlled by adjusting the feedback gain, and frequencies can be made nearly independent of amplitude fluctuations. Quantum jump spectroscopy of a perpendicular cyclotron motion reveals the absolute temperature and amplitude of the self-excited oscillation. The possibility to quickly measure parts per billion frequency shifts could open the way to improved measurements of e(-), e(+), p, and (-)p magnetic moments.
The measurement of the anomalous electron magnetic moment g−2g-2g−2 through quantum transitions of a single trapped electron is the most stringent test of quantum field theory. These experiments are now so precise that they must account for the effects of the cavity containing the electron. Classical calculations of this "cavity shift" must subtract the electron's divergent self-field, and thus require knowledge of the exact Green's function for the cavity's electromagnetic field. We perform the first fully quantum calculation of the cavity shift in a closed cavity, which instead involves subtracting linearly divergent cavity mode sums and integrals. Using contour integration methods, we find perfect agreement with existing classical results for both spherical and cylindrical cavities, justifying their current use. Moreover, our mode-based results can be naturally generalized to account for systematic effects, necessary to push future measurements to the next order of magnitude in precision.