Attosecond theory

 

In the high-intensity regime (I>10¹⁶W/cm²), Fermi's golden rule is fully inadequate for calculating ionization yields. Therefore, several alternative methods are used, some of which (mainly numerical) predict the existence of ``atomic stabilization'' (i.e the decrease of the ionization probability with the field intensity) for atoms subject to short-pulsed laser radiation [1]. The existence of this phenomenon is one of the most controversial issues of super-intense laser-atom physics, and, since there are no experiments in the intensity and frequency regimes for which stabilization may occur, the problem is not settled yet. The strongest experimental evidence is presented in [2], where the ionization probability as a function of the field strength appears to saturate towards a finite value smaller than one. However, these experiments are performed for much lower intensities than those for which the theoretical predictions are made. Not only its existence, but also the physical mechanisms originating this phenomenon and the conditions for its occurrence have raised considerable debate. Most numerical studies suggest that stabilization occurs for high-frequency pulses which are smoothly switched-on or off, but no rigorous criteria exist.

 Using analytical methods, we derive a rigorous proof for the existence of stabilization and establish mathematical criteria for its existence or absence. We show that stabilization exists when the classical momentum transfer from the field to the electron and the classical displacement vanish at the end of the pulse. Our methods are:

• Bounds:

We calculate upper and lower bounds for the ionization probability. Taking a realistic system, namely Hydrogen, and several pulse shapes, we show that stabilization is always absent for non-vanishing momentum transfer at the end of the pulse, regardless of the pulse shape or how smoothly it is switched on or off. This method permits an analytical treatment of the problem also at the turn-on and off regions.
• Gordon Volkov(GV) perturbation theory:

Instead of taking the external field as a perturbation, we take the binding potential. Clearly, this method is not expected to work well in the turn-on and off regions, but the asymptotic behavior of the GV series when the field strength or the frequency goes to infinity yields useful information on the absence or presence of stabilization. For vanishing momentum transfer and classical displacement at the end of the pulse we obtain qualitatively similar results as in the experiments [2].

Furthermore, we establish alternative criteria for the existence or absence of stabilization from the scaling behavior of the ionization probability.

• My contributions to the subject

See also:
 
• A. Fring, J. Kostrykin and R. Schrader, ``On the absence of bound-state stabilization through short ultra intense fields", J. Phys. B 29, 5651 (1996)
• A. Fring, J. Kostrykin and R. Schrader, ``Ionization probabilities through ultra-intense fields in the extreme limit", J. Phys. A 30, 8599 (1997)
• My collaborators: A. Fring , R. Schrader

References:
[1] For reviews, see e.g. J.H. Eberly and K. C. Kulander, Science 262, 1229 (1993); S. Geltman, Chem. Phys. Lett. 237, 286 (1995)
[2] N.J. van Druten et al, Phys. Rev. A 55, 622 (1997)