A Method for Measuring the $6S_{1/2} \leftrightarrow 5D_{3/2}$ Magnetic Dipole Transition Moment in {Ba}$^{+}$

TL;DR

This paper proposes a novel method to measure the magnetic dipole transition moment in Ba$^{+}$ ions, which is essential for parity nonconservation experiments and testing atomic many-body theory.

Contribution

The paper introduces an adapted measurement technique for the M1 transition moment in Ba$^{+}$, enabling experimental verification of theoretical calculations and aiding parity violation studies.

Findings

Proposed a measurement method based on symmetry differences in E2 and M1 couplings.

Calculated the M1 transition moment dominated by electron-electron correlation effects.

Highlighted the importance of experimental verification for theoretical M1 values.

Abstract

We propose a method for measuring the magnetic dipole (M1) transition moment of the $6S_{1/2} \big(\mathrm{m}=-1/2\big)\leftrightarrow 5D_{3/2}\big(\mathrm{m}=-1/2\big)$ transition in single trapped Ba$^{+}$ by exploiting different symmetries in the electric quadrupole (E2) and M1 couplings between the states. The technique is adapted from a previously proposed method for measuring atomic parity nonconservation in a single trapped ion [Norval Fortson, Phys. Rev. Lett. \textbf{70}, 17 (1993)]. Knowledge of M1 is crucial for any parity nonconservation measurement in Ba$^{+}$, as laser coupling through M1 can mimic the parity-violating signal. The magnetic moment for the transition has been calculated by atomic theory and found to be dominated by electron-electron correlation effects [B.K. Sahoo et. al., Phys. Rev. A \textbf{74}, 6 (2006)]. To date the value has not been verified experimentally. This proposed measurement is therefore an essential step toward a parity nonconservation experiment in the ion that will also test current many-body theory. The technique can be adapted for similar parity nonconservation experiments using other atomic ions, where the magnetic dipole moment could present similar complications.