Theoretical derivation of laser-dressed atomic states by using a fractal space: application to ionization by XUV pulses

Guillaume Duchateau

Published 2017-03-06Version 1

The derivation of approximate wave functions for an electron submitted to both a coulomb and a laser electric fields, the so-called Coulomb-Volkov (CV) state, is first addressed. Despite its derivation for continuum states does not exhibit particular difficulty within the framework of the standard theory of quantum mechanics (QM), difficulties arise when considering an initially bound atomic state. The natural way of translating the unperturbed momentum by the laser vector potential is no longer possible since a bound state does not exhibit a plane wave form including explicitely a momentum. The use of a fractal space allows one to naturally define a momentum for a bound wave function. Within this framework, it is shown how the derivation of laser-dressed bound states can be performed. Based on a generalized eikonal approach, a new expression for the laser-dressed states is also derived, fully symmetric relative to the continuum or bound nature of the initial wave function. It includes an additional crossed term in the Volkov phase which was not obtained within the standard theory of quantum mechanics. The derivations within this fractal framework have highlighted other possible ways to develop approximate laser-dressed states in QM. In particular, a more general CV state including an additional phase pertaining to the acceleration gauge is derived. After comparing the various obtained wave functions, the generalized CV state is used to predict the ionization probability of hydrogen targets by attosecond XUV pulses within the sudden approximation. This simple approach allows to make predictions in various regimes depending on the laser intensity, going from the non-resonant multiphoton absorption to tunneling and barrier-suppression ionization.