Proposal for parity nonconservation measurements in a single trapped Ba ion

The interaction of the weak neutral currents between the atomic nucleus and electrons through the exchange of $Z_{o}$ Bosons results in parity violations in atomic systems. The precision of a single Ba$^+$ parity nonconservation (PNC) experiment is predicted to be 0.13{\%} (three fold improvement over the recent atomic PNC measurements in Cs [1]). This combined with the atomic theory of Ba$^+$ will act as a means to test the electroweak physics. We propose to measure the parity violation in Ba$^+$ by coherently exciting the transition $6S_{1/2} \leftrightarrow 5D_{3/2} $ with a 2051 nm laser. Interference between $E1_{PNC} $ (non-vanishing electric dipole transition amplitude between transition $6S_{1/2} \leftrightarrow 5D_{3/2} )$ and $E2$ (electric quadrupole transition amplitude) or $M1$ (magnetic dipole transition amplitude) gives a measure of the parity violating light shifts. Controlling the polarization of the 2051 nm laser and measuring the associated Rabi frequency in each case enables the extraction of $E1_{PNC} $ and $E2/M1$ amplitude from these measurements.\\[4pt] [1] Phys. Rev. Lett. \textbf{82}, 2484