Wavelength scaling of strong-field Rydberg-state excitation: Toward an effective S -matrix theory

Abstract

$S$-matrix theory and the Born expansion, the lowest-order term of which is known as the ``strong-field approximation'' (SFA), play an indispensable role in our understanding of atomic and molecular processes in intense laser fields. Most phenomena in this field are reproduced by the first two terms of the Born series. However, for a long-range potential such as the Coulomb potential, the second-order term may be larger than the SFA term, raising the problem of the convergence of the Born series. By simultaneously measuring and simulating ionization and Rydberg-state excitation of an argon atom subject to a strong laser field for various wavelengths, we demonstrate that the wavelength scaling law of the measured ratio of ${\mathrm{Ar}}^{*}$ over ${\mathrm{Ar}}^{+}$ and the period of its oscillation with respect to the laser intensity can be well reproduced by the second-order term of the $S$-matrix expansion in terms of the Coulomb potential, but not by the lowest-order (SFA) term. We conjecture that the second-order term of the $S$-matrix expansion may provide an effective theory for the intense-laser--atom interaction.