Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback

This paper reports two pump-probe experiments in sodium where dynamically tailored ultrashort pulses from a Ti:Sapphire-pumped optical parametric amplifier were employed. The first study focuses on the one-photon Na(3s --> 3p) transition to derive sensitive criteria which judge the performance of a frequency-domain pulse shaper using a spatial light modulator. On the basis of the interpretation, follow-up experiments are suggested to test their cogency. The second experiment uses coherent quantum control by placing an appropriate phase distribution on the incident beam to enhance or cancel the transition probability in the nonresonant two-photon process Na(3s -->--> 5s). Ignorant of the "ideal" phase function, an evolutionary algorithm which uses a feedback derived from the experiment performs the optimization and produces the desired bright or dark pulses within a few minutes. Attention is given to the role of resonant 3s --> 3p transitions excited by the spectral wings of the pump pulse. Different parametrizations of the phase distribution have been examined. Two of these produced solutions which had not previously been predicted by theory still meet the objective of the experiment. The study represents the first successful application of a feedback-organized self-learning algorithm to the design of dark pulses.