DETECTION AND CONTROL OF MOLECULAR QUANTUM DYNAMICS

We combine a theory of quantum control in the weak-response regime wit h the conventional theory of pump-probe spectroscopy, in order to prov ide a clear theoretical basis for control experiments of the type rece ntly carried out in our group. In the control scenario considered here , we compute the pump field that best drives a quantum system to a des ired target or goal. To monitor the temporal evolution of the quantum system, we employ an optical scheme in which the wave packet created b y the pump, or control, field is probed with a second ultrafast pulse to a higher-lying electronic state. The absorption of the probe pulse is proportional to the laser-induced fluorescence (LIF) signal observe d in an experiment and thus gives a measure of the quantum distributio n of the wave packet in the target region. By using a series of such p robe pulses at different times and/or different photon energies, the q uantum temporal evolution of the control system can be mapped out. Num erical examples are presented for the control and subsequent detection of the vibrational dynamics of the I-2 molecule on an electronically excited potential energy surface. By comparing the LIF signal for the globally optimal field for a specific target with the signal obtained from a deliberately nonoptimal field, the time reversal of the optimal field, which has the same frequency spectrum, we demonstrate that a c lear signature of control can be obtained by monitoring a spectroscopi c observable. Finally, we compare the detected signal as computed by e xact quantum mechanics and as approximated by the computationally simp ler classical Condon approximation.