Distinction of different two-photon transition pathways by spatial coherent control

The spatial coherent control of resonant two-photon transitions in atomic rubidium using counter-propagating ultra-short laser pulses is investigated in this work. There are two transition pathways involved in the spatial excitation pattern. A special pulse shaping scheme is designed to distinguish their individual contribution. The scheme consists of a n-step function flipping at the poles and zeros of the transition amplitude function and two segmented linear function with different slopes, and it can make the desired transition pathway dominate at the assigned spatial position. The simulations show that our scheme is quite effective compared to the previous single linear shaping scheme.