Theories of photoelectron correlation in laser-driven multiple atomic ionization

Experimental advances with laser intensities above 1 TW/cm^2, with pulse durations between roughly 50 and 5 fs, have led to the discovery of new atomic effects that include examples of startlingly high electron correlation. These phenomena have presented an unexpected theoretical challenge as they lie outside the domains of both of the nominally applicable theories, namely, straightforward perturbative radiation theory and quasistatic tunneling theory. The two liberated electrons present a new few-body collective effect. When they are not released independently, one by one, the term nonsequential double ionization has been adopted. Theoretical avenues of attack have emerged in two categories, which are strikingly different. They can be labeled as ``all-at-once'' and ``step-by-step'' approaches. Although different, even conceptually opposite in some ways, both approaches have been successful in confronting substantial parts of the experimental data. These approaches are examined and compared with their results in addressing key experimental data obtained over the past decade.