Multiphoton ionization in a short-range potential: A nonperturbative approach

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Abstract
We introduce an alternative approach to the study of multiphoton ionization. The approach is based on consideration of the relative frequency instead of the relative field strength of the applied laser field as a small parameter (or, equivalently, a large number of photons). The choice is based on the characteristics of present-day lasers. We apply our approach specifically to an electron bound by a δ-function potential. In order to show a simpler situation first, we start by applying our analysis to the time-independent tunneling problem from such a potential due to an external electrostatic field. For this problem, we derive from first principles the well-known ionization rate for tunneling. Next, we derive with the same general formalism an analytical formula, asymptotic in the number of photons, for the multiphoton ionization rate, under strong field conditions, of an electron confined by a δ-function potential. We also obtain the ionization rate from a numerical solution of the corresponding equations. The comparison with the analytical expression is very good, even for a small number of photons. Our approach puts the results of Perelomov, Popov, and Terentev (Zh. Eksp. Teor. Fiz. 50, 1393 (1966) [Sov. Phys. JETP 23, 924 (1966)]) on a rigorous basis as well as extending them to a wider range of parameters. To cover analytically the few-photon case, we also develop a perturbation theory in the relative field strength to calculate the ionization rate. This perturbative approach has the advantage over the conventional Rayleigh-Schrödinger theory in that it effectively takes into account the continuum without having to deal with it directly. The comparison with the numerical results is also very good.