Theoretical derivation of laser-dressed atomic states by using a fractal space

TL;DR

This paper introduces a fractal space framework to derive laser-dressed atomic states, addressing the challenge of defining momentum for bound states, and applies it to predict hydrogen ionization probabilities under intense laser fields.

Contribution

It presents a novel fractal space approach for deriving laser-dressed bound states, including a generalized eikonal method and a new symmetric wave function expression.

Findings

Derived new laser-dressed state expressions including a crossed phase term.

Compared various wave functions and validated predictions for hydrogen ionization.

Predicted ionization regimes from multiphoton to tunneling using the new framework.

Abstract

The derivation of approximate wave functions for an electron submitted to both a coulomb and a time-dependent laser electric fields, the so-called Coulomb-Volkov (CV) state, is addressed. Despite its derivation for continuum states does not exhibit any particular problem within the framework of the standard theory of quantum mechanics (QM), difficulties arise when considering an initially bound atomic state. Indeed 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 permits 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 unperturbed 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 derive approximate laser-dressed states in QM. After comparing the various obtained wave functions, an application to the prediction of the ionization probability of hydrogen targets by attosecond XUV pulses within the sudden approximation is provided. This 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.