On the potential for high-accuracy spectroscopy of $\mathrm{H}_2^+$ and $\overline{\mathrm{H}}_2^-$ in Penning traps for a test of CPT invariance

TL;DR

This paper analyzes the feasibility of high-precision spectroscopy of $ ext{H}_2^+$ and $ ext{H}_2^-$ in Penning traps to test CPT invariance, proposing methods to achieve fractional frequency measurement accuracy of 10^{-17}.

Contribution

It provides an extensive analysis of laser spectroscopy proposals in Penning traps, introduces novel implementation aspects, and estimates achievable accuracy for CPT tests using existing technology.

Findings

Fractional frequency comparison accuracy of 10^{-17} is feasible.

Analysis of implementation methods with continuous Stern-Gerlach or quantum-logic spectroscopy.

Complementary CPT tests via g-factor and magnetic moment measurements.

Abstract

The comparison of vibrational transition frequencies of $\mathrm{H}_2^+$ and $\overline{\mathrm{H}}_2^-$ offers a new opportunity to test CPT invariance. Myers [Phys. Rev. A 98, 010101(R) (2018)] proposed performing laser spectroscopy in a Penning trap (PT) with non-destructive read-out. Here, we provide an extensive analysis of this proposal, introduce novel aspects, and discuss its implementation in PTs that incorporate either the continuous Stern-Gerlach effect or quantum-logic spectroscopy. We derive estimates for the achievable accuracy of the test. We find that a comparison of the vibrational frequencies at a fractional level of $1\times10^{-17}$ is a realistic prospect, using technology that is mostly already available. We also analyze complementary CPT invariance tests, namely those of the g-factor of the bound electron/positron via electron-spin-resonance spectroscopy and of the magnetic moment of the proton/antiproton via radiofrequency spectroscopy.