Quantum Calculations of the Cavity Shift in Electron Magnetic Moment Measurements

TL;DR

This paper presents the first fully quantum calculation of the cavity shift affecting electron magnetic moment measurements, confirming classical results and enabling more precise future experiments.

Contribution

It introduces a quantum approach to compute the cavity shift, aligning with classical results and facilitating systematic effect analysis for enhanced measurement accuracy.

Findings

Quantum calculation matches classical cavity shift results

Method can be extended to systematic effect analysis

Supports higher-precision electron magnetic moment experiments

Abstract

The measurement of the anomalous electron magnetic moment $g-2$ 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.