Nuclear dynamics phase effects

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

Fig. 4.8. (a) The measured (squares) and predicted (thick lines) intensity ratio r(q) between harmonics from H2 and that from D2 molecules as functions of harmonic order q. tqm and rcM are the predictions with and without quantum effect for nuclear dynamics see text, (b) The measured (squares) and predicted (thick line) relative phases between harmonics from H2 and those from D2 molecules as functions of harmonic order q. Measuring the relative phases directly corresponds to observing the nuclear motions, i.e., the nuclear displacement of H2 Aii1 2 (right axis) as a function of excursion time r (superior axis). For (a) and (b), vertical and horizontal errors represent SEM for 800 laser shots and those from quantum mechanical uncertainty [27]... 

All approaches for the description of nonadiabatic dynamics discussed so far have used the simple quasi-classical approximation (16) to describe the dynamics of the nuclear degrees of freedom. As a consequence, these methods are in general not able to account for processes or observables for which quantum effects of the nuclear degrees of freedom are important. Such processes include nuclear tunneling, interference effects in wave-packet dynamics, and the conservation of zero-point energy. In contrast to quasi-classical approximations, semiclassical methods take into account the phase exp iSi/h) of a classical trajectory and are therefore capable—at least in principle—of describing quantum effects. 

Switching electronic population to different final states with high efficiency via SPODS is a fundamental resonant strong-field effect as the only requirement is the use of intense ultrashort laser pulses exhibiting temporally varying optical phases, such as phase jumps [67, 68, 70, 71] or chirps [44, 72]. Only recently, these concepts were transferred to molecules, where the coupled electron-nuclear dynamics have to be considered in addition [73,74]. 

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