Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses

Multiphoton transitions can be reached by many routes through a continuum o f virtual levels. We show that the transition probability of two-photon and multiphoton processes can be controlled by tailoring the shape of an ultra short excitation pulse, so that the many paths leading to the final state i nterfere to give a desired probability amplitude. We analyze the effect of pulse shapes on N-photon absorption as well as on Raman transitions. We sho w theoretically that certain tailored dark pulses do not excite the system at all, while other shaped pulses induce transitions as effectively as tran sform limited pulses, even when their peak amplitudes are greatly reduced. These results are confirmed experimentally for two-photon transitions in at omic cesium. [S1050-2947(99)00808-2].