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Recently the time evolution of atomic photoionization by an intense few-cycle laser pulse has been studied in a kind of pump-probe experiment with attosecond XUV pulses (Uiberacker et al. 2007 Nature 446, 627, Uphues et al 2007 NJP, submitted). We develop a theoretical description of such experiments. A possible modification of the recent attosecond tunneling experiment is proposed, which consists in measuring the yield of the doubly-charged Li ions produced by the combined action of a strong few-cycle infrared pulse and an ultrashort (attosecond) extreme ultraviolet (XUV) pulse. We predict the results of such attosecond chronoscopy experiment, basing on the numerical solution of the time-dependent Schrödinger equation, which describes the atomic electron in a strong laser field. The influence of the XUV pulse is treated in the sudden approximation. It is shown that the dependence of the double ionization cross section on the time delay between the two pulses reflects the time evolution of the strong-field ionization. We demonstrate that even more detailed information can be gained from the forward-backward asymmetry of the photoelectron emission. With the same model we explain qualitatively the characteristic features of the above mentioned experiment on Ne and predict some new effects which can be observed in attosecond chronoscopy experiments with better time-resolution.
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