Inertial and gravitational effects on a geonium atom

Abstract

We reveal all linear order inertial and gravitational effects on a non-relativistic Dirac particle (mass $m$) on the Earth up to the order of $1/m$ in the Foldy-Wouthuysen-like expansion. Applying the result to Penning trap experiments where a Dirac particle experiences the cyclotron motion and the spin precession in a cavity, i.e., a geonium atom, we study modifications to the $g$-factor of such as the electron. It is shown that each correction from gravity has different dependence on the cyclotron frequency and the mass $m$. Therefore, their magnitude change depending on situations. In a particular case of an electron $g$-factor measurement, the dominant correction to the observed $g$-factor comes from effects of the Earth's rotation, which is $\delta g/2\simeq 5.2\times 10^{-17}$. It may be detectable in the near future.

23 pages, 2 figures, 1 table, typos corrected, minor changes

References in corpus (4)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• The anomalous magnetic moment of the muon in the Standard Model
• Hermiticity of the Dirac Hamiltonian in Curved Spacetime
• A formalism for magnon gravitational wave detectors

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• Probing high-frequency gravitational waves with entangled vibrational qubits in linear Paul traps
• Quantum sensing of high-frequency gravitational waves with ion crystals