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We demonstrate the use of the ultrafast spatial coherent-control method toresolve the fine-structure two-photon transitions of atomic rubidium.Counter-propagating ultrafast optical pulses with spectral phase and amplitudeprogrammed with our optimized solutions successfully induced the two-photontransitions through $5S_{1/2}$-$5P_{1/2}$-$5D$ and $5S_{1/2}$-$5P_{3/2}$-$5D$pathways, both simultaneously and at distinct spatial locations. Threedifferent pulse-shaping solutions are introduced that combine amplitudeshaping, which avoids direct intermediate resonances, and phase programming,which enables the remaining spectral components to be coherently interferedthrough the targeted transition pathways. Experiments were performed with aroom-temperature vapor cell, and the results agree well with theoreticalanalysis.

Doppler-free coherent-control spectroscopy with a colliding pair of shaped pulses