This paper explores the benefit of using time dependent basis sets in the description of adiabatic population transfer between molecular states. Using a time dependent basis set formalism, we develop a counter-diabatic field paradigm that generates adiabatic population transfer for apparently unfavorable conditions. We also describe a time dependent perturbation approach to account for the effect of stochastic dephasing on adiabatic population transfer.

We report the results of studies of various aspects of the counter diabatic field paradigm, a recipe that generates adiabatic population transfer between levels by assisting a given field so that the total field generates the population transfer that the adiabatic approximation suggests for the given field. The sensitivity of this recipe to the pulse parameters and to Gaussian stochastic phase fluctuations between the fields has been investigated. Ladder-climbing population transfer between the vibrational levels of a nonrotating Morse oscillator is examined, and a numerical demonstration of the efficiency of the scheme is given.

The control of population transfer can be affected by the adiabatic evolution of a system under the influence of an applied field. If the field is too rapidly varying or too weak, the conditions for adiabatic transfer are not satisfactorily met. We report the results of an analysis of properties of counterdiabatic fields (CDFs) that restore the adiabatic dynamics of a system by suppressing diabatic effects as they are generated. We observe that a CDF is not unique and find the one that has minimum intensity, and we provide natural upper and lower bounds to the integrated intensity of a CDF in terms of integrals of the eigenvalues of the system Hamiltonian. For Hamiltonians that are separable with respect to their parameters, we prove that the time integral of an associated CDF is path independent. Finally we explain why and when, in the neighborhood of an avoided crossing, a CDF can be approximated by Lorentzian pulses.

We report the results of a study of the influence of solvent fluctuations on the efficiency of selective population transfer from an initial state to a designated target state of a solute molecule. Our model of the influence of liquid fluctuations on the states of the solute assumes that dephasing is the dominant relaxation process, and utilizes an analog of the Kubo stochastic theory of line shape. The solvent fluctuations are represented as a Gaussian random process that independently modulates each of the energy levels of the solute molecule. For typical liquid densities the maximum amplitude of these fluctuations is taken to be of the order of 150 cm−1, and the correlation time of the fluctuations is taken to be of the order of a few hundred femtoseconds, but we have also explored the effects of varying the fluctuation frequency and correlation time. It is shown that STIRAP (stimulated Raman adiabatic passage) generated population transfer to a designated target state of the solute remains efficient when the frequency of the solvent fluctuations is large or small relative to the inverse of the widths of the pump and Stokes pulses. It is further shown that extended STIRAP generated selective transfer to one of a pair of degenerate states of the solute remains efficient under the same conditions. These results suggest, subject to the accuracy of the representation of the influence of the solvent on the solute, that it should be possible, using coherent superpositions of states generated with picosecond excitation, to control population transfer, hence reactivity, for a class of reactions carried out in the liquid phase.

We report the results of simulation studies of the statistics of vibrational dephasing of a YCl (Y=H, D, T, and I) diatom in dense fluid Ar at two temperatures, including the effect of strong field driving on the energy level modulation statistics. The distribution of energy level modulations is found to be non-Gaussian with a high energy tail. Aspects of stimulated Raman adiabatic passage (STIRAP) between the vibrational levels of HCl in dense fluid Ar have been investigated. For HCl with nearly degenerate v=0-->v=1 and v=1-->v=2 transitions, the combined effect of modulation and power broadening reduces the STIRAP efficiency for population transfer from v=0 to v=2 of the order of 30%. However, if the transitions used have very different frequencies, as in the original model studied by Demirplak and Rice [J. Chem. Phys. 116, 8028 (2002)], the STIRAP efficiency for population transfer remains high, of the order of 80%, even with non-Gaussian modulation of energy levels.