DETECTION AND CONTROL OF MOLECULAR QUANTUM DYNAMICS

We combine a theory of quantum control in the weak-response regime with the conventional theory of pump-probe spectroscopy, in order to provide a clear theoretical basis for control experiments of the type recently carried out in our group. In the control scenario considered here, we compute the pump field that best drives a quantum system to a desired target or goal. To monitor the temporal evolution of the quantum system, we employ an optical scheme in which the wave packet created by 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 observed in an experiment and thus gives a measure of the quantum distribution of the wave packet in the target region. By using a series of such probe pulses at different times and/or different photon energies, the quantum temporal evolution of the control system can be mapped out. Numerical 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 clear signature of control can be obtained by monitoring a spectroscopic observable. Finally, we compare the detected signal as computed by exact quantum mechanics and as approximated by the computationally simpler classical Condon approximation.