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

This paper reports two pump-probe experiments in sodium where dynamically t ailored ultrashort pulses from a Ti:Sapphire-pumped optical parametric ampl ifier 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 c ogency. The second experiment uses coherent quantum control by placing an a ppropriate 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 whic h 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 spec tral wings of the pump pulse. Different parametrizations of the phase distr ibution have been examined. Two of these produced solutions which had not p reviously been predicted by theory still meet the objective of the experime nt. The study represents the first successful application of a feedback-org anized self-learning algorithm to the design of dark pulses.