Introduction

Thanks to the recent remarkable progress of laser technology, it has become meaningful and useful to investigate the possibilities of manipulating molecular processes and chemical dynamics by lasers. Various ideas have been proposed so far[1−9]. Typical examples are (i) coherent control in which quantum mechanical interference effect is used to control the branching ratio into the desirable final product, (ii) pump−dump method in which a wave packet is pumped or dumped by laser at appropriate positions to achieve a desirable product, (iii) linear chirping in which the laser frequency is linearly varied as a function of time to attain high efficiency, (iv) various kinds of adiabatic rapid passage that represent applications of linear chirping, and (v) optimal control theory which tries to control wave packet dynamics optimally. Among these, we have especially noticed the significance of non-adiabatic transitions induced by lasers. If the laser frequency ω is not low (< 1000 cm−1), the Floquet (or dressed) state representation holds well and molecular potential energy curves or surfaces are shifted up or down by the amount of laser energy ħω[10]. This means that potential curve (or surface) crossings are created among these states. The interaction between the crossing states is equal to −με/2, where μ is the transition dipolemoment and ε is the amplitude of the laser field.

The time-dependences of the frequency ω(t) and the pulse envelope ε(t), which are supposed to be much slower than the time-dependence of the field oscillation exp(i ʃt ω(t)dt), cause time-dependent non-adiabatic transitions. The time-dependence of ω(t) induces the time-dependent Landau−Zener type non-adiabatic transition and the time-dependence of ε(t) induces the time-dependent Rosen−Zener type non-adiabatic transition[9]. In the case of CW (continuous wave) laser, on the other hand, both ω and ε are constant and potential curve crossings are created along the molecular spatial coordinate, i.e., the internuclear distance. Non-adiabatic transitions are generally well localized at avoided crossings between adiabatic states regardless of whether they are time-dependent or time-independent, and molecular processes can be nicely described as a sequence of adiabatic wave propagations along adiabatic states and non-adiabatic transitions at avoided crossings.