Electronic phase-locking for three-color, two-pathway coherent control

We report a new method of two-pathway coherent control using three narrow-band cw laser sources, phase locked in an optical phase-lock loop, to maintain the high degree of optical coherence required for the coherent control process. In addition, we derive expressions for two-photon transition amplitudes and demonstrate their dependence on the polarization of the field components. This phase-locking technique expands the set of interactions to which coherent control techniques may be applied. It also allows for a constant low-frequency offset between the optical interactions, producing a continuous and constant phase ramp between the interactions, facilitating phase-sensitive detection of the modulating atomic signal. We illustrate this technique with two-photon vs.~one-photon excitation of a $\Delta F = 1$ component, and alternatively a $\Delta F = 0$ component, of the $6s \: ^2S_{1/2} \rightarrow 7s \: ^2S_{1/2}$ transition of atomic cesium.