Molecular systems, quantum interference atomic transitions

The effect of quantum interference on spontaneous emission in atomic and molecular systems is the generation of superposition states that can be manipulated, to reduce the interaction with the environment, by adjusting the polarizations of the transition dipole moments, or the amplitudes and phases of the external driving fields. With a suitable choice of parameters, the superposition states can decay with controlled and significantly reduced rates. This modification can lead to subnatural linewidths in the fluorescence and absorption spectra [5,10]. Furthermore, as will be shown in this review, the superposition states can even be decoupled from the environment and the population can be trapped in these states without decaying to the lower levels. These states, known as dark or trapped states, were predicted in many configurations of multilevel systems [11], as well as in multiatom systems [12],... 

This represents a formidable practical problem, as one is very unlikely to find isolated atoms with two nonorthogonal dipole moments and quantum states close in energy. Consider, for example, a V-type atom with the upper states 11), 3) and the ground state 2). The evaluation of the dipole matrix elements produces the following selection rules in terms of the angular momentum quantum numbers J — J2 = 1,0, J3 — J2 = 1,0, and Mi — M2 = M3 — M2 = 1,0. Since Mi / M3, in many atomic systems, p12 is perpendicular to p32 and the atomic transitions are independent. Xia et al. [62] have found transitions with parallel and antiparallel dipole moments in sodium molecules (dimers) and have demonstrated experimentally the effect of quantum interference on the fluorescence intensity. We discuss the experiment in more details in the next section. Here, we point out that the transitions with parallel and antiparallel dipole moments in the sodium dimers result from a mixing of the molecular states due to the spin-orbit coupling. 

In summary, Miller s 1970 papers [1, 2] on classical 5-matrix theory had a profound influence on the theory of molecular collisions and related topics such as photodissociation. Following earlier work on elastic scattering, they demonstrated how the results of classical mechanics can be built into a quantum mechanical framework of inelastic collisions. In my view the greatest asset of the classical 5-matrix theory is its interpretative power. The general shape of transition probabilities or collisional cross sections can be easily understood in terms of classical trajectories and their quantum mechanical interference. Exact quantum mechanical programs are like black boxes and the results are often difficult to understand without the help of classical mechanics or semiclassical analyses. The new developments such as the IVR are likely to become major tools for systems consisting of many atoms. 

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