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Atomic stabilization in superintense laser fields

Atomic stabilization is a highlight of superintense laser–atom physics. A wealth of information has been gathered on it; established physical concepts have been revised in the process; points of contention have been debated. Recent technological breakthroughs are opening exciting perspectives of experimental study. With this in mind, we present a comprehensive overview of the phenomenon. We discuss the two forms of atomic stabilization identified theoretically. The first one, ‘quasistationary (adiabatic) stabilization’ (QS), refers to the limiting case of plane-wave monochromatic radiation. QS characterizes the fact that ionization rates, as calculated from single-state Floquet theory, decrease with intensity (possibly in an oscillatory manner) at high values of the field. We present predictions for QS from various forms of Floquet theory: high frequency (that has led to its discovery and offers the best physical insight), complex scaling, Sturmian, radiative close coupling and R-matrix. These predictions all agree quantitatively, and high-accuracy numerical results have been obtained for hydrogen. Predictions from non-Floquet theories are also discussed. Thereafter, we analyse the physical origin of QS. The alternative form of stabilization, ‘dynamic stabilization’ (DS), is presented next. This expresses the fact that the ionization probability at the end of a laser pulse of fixed shape and duration does not approach unity as the peak intensity is increased, but either starts decreasing with the intensity (possibly in an oscillatory manner), or flattens out at a value smaller than unity. We review the extensive research done on one-dimensional models, that has provided valuable insights into the phenomenon; two- and three-dimensional models are also considered. Full three-dimensional Coulomb calculations have encountered severe numerical handicaps in the past, and it is only recently that a comprehensive mapping of DS could be made for hydrogen. An adiabatic variation of the laser-pulse envelope keeps the system in the Floquet state associated with the initial state, that allows calculation of the ionization probability in terms of the corresponding rate. A nonadiabatic variation can excite other Floquet states, either discrete (‘shake-up’) or continuous (‘shake-off’), with considerable consequences for DS. A unitary interpretation of these aspects of DS is presented in terms of ‘multistate Floquet theory’. We then comment on the points of contention raised in connection with DS. Further, we review the extent to which the classical approach has been successful in describing DS. We next examine the concern that nonrelativistic (NR) predictions for stabilization may be inadequate in superintense fields, because relativistic corrections would invalidate them. It turns out that, although the relativistic corrections do limit stabilization, there is an ample ‘window’ of intensities for which the NR predictions remain valid. Finally, we discuss the experimental evidence in favour of stabilization. For lack of adequate lasers to study ground states of single-active-electron atoms, the experiments so far have been performed on low-lying Rydberg states. Two state-of-the-art experiments have determined ionization yields for pulses with adiabatic envelopes. Their results concur, are in agreement with the theoretical predictions and represent a clear-cut confirmation of DS. Our conclusion is that superintense field stabilization is firmly established, both theoretically and experimentally. Nevertheless, further research is desirable to solve interesting open problems, some of which we identify. Their research is made timely by the superintense high-frequency light sources that are being developed, such as VUV-FELs, or attosecond pulses from high-harmonic generation.