Quantum Calculations of the Cavity Shift in Electron Magnetic Moment Measurements

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.

41+16 pages, 7 figures. v2: discussion expanded, matches journal version

References in corpus (7)

• Measurement of the fine-structure constant as a test of the Standard Model
• Measurement of the Electron Magnetic Moment
• Direct high-precision measurement of the magnetic moment of the proton
• Electronic detection of charged particle effects in a Penning trap
• Foldy-Wouthuysen Transformation in Strong Magnetic Fields and Relativistic Corrections for Quantum Cyclotron Energy Levels
• Quantum Electrodynamic Corrections to Cyclotron States in a Penning Trap
• Quantum Logic Spectroscopy of an Electron and Positron for Precise Tests of the Standard Model