Gain measurement scheme for precise determination of atomic parity violation through two-pathway coherent control

Precision measurements of parity non-conserving (PNC) interactions in atoms, molecules and ions can lead to the discovery of new physics beyond the standard model and understanding of weak-force induced interactions in the nucleus. In this paper, we propose and analyze a novel atomic parity violation measurement scheme for a forbidden transition where we combine a two-pathway coherent control mechanism with probe gain techniques. We detail a feasible experimental geometry for $6S_{1/2}\rightarrow 7S_{1/2}$ transitions in a cesium vapor cell, and consider the statistical noise of such a measurement under reasonable laboratory conditions. We estimate the signal-to-noise ratio to be approaching $\sim2.3/\sqrt{Hz}$. This scheme, with low expected systematic errors, would allow for precise measurements in cesium and other heavy metal systems.