Analysis of two-pathway coherent control for precision measurement of weak optical transitions

We present a new technique based on two-pathway optical coherent control for the sensitive detection and precise measurement of highly-forbidden transitions in atomic systems. Specifically, we show that ($\omega$, 2$\omega$) coherent control can be applied to the measurement of the magnetic dipole and electroweak parity nonconserving amplitudes in atomic cesium, with the principal advantage of reduced systematic errors related to field reversals often encountered in previous measurements of these effects. We present a complete analysis in one specific geometry, and discuss prospects for improved laboratory determinations of these weak transition amplitudes.