Atoms in high AC fields

We return now to a problem introduced in section 9.26, namely the dynamics of excitation by a very short pulse laser of high intensity. This has been studied [584] by two different theoretical approaches. First, quantum calculations plotted frame by frame at different times during the laser pulse reveal how the composition of the eigenstates varies and how the system may re-emerge either in an excited state or return to the original composition depending on the laser parameters (see figs. 10.14 and 10.15). 

Second, calculations can be performed in a semiclassical regime, and the results plotted on a Poincare section in action-angle (I, 0) coordinates. Such diagrams may seem complicated (see figs. 10.16 and 10.17), but are at least in principle readily understood a near-horizontal line across the (1,0) plot corresponds to a torus in ordinary phase space. When periodically extended in the time coordinate, each line corresponds to a vortex tube embedded in the extended phase space of the periodically 

These calculations reveal another interesting property. As the complexity of the plots increases, chaotic trajectories appear, which grow (as expected) from the separatrix outwards. The presence of such orbits heralds new paths for ionisation, which may eventually dominate the whole of phase space. 

It is clear from such calculations that the dynamics are very complex, but that they do depend on the nature of the system being studied. The major difficulty is to unravel the map of avoided crossings for a given system. It is at this level that one may expect an interplay between the correlating effects of the ponderomotive field itself and electron-electron 

We can now summarise the situations which occur after irradiation of an atom or molecule by a strong field laser pulse  

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