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

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 laserdressed 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.

Resolution-scale relativistic formulation of non-differentiable mechanics

“…At the same time, it seems to provide an avenue to extend the reach of fundamental physics methods to integrate complex and chaotic systems, the approaches to which are otherwise restricted to effective and phenomenological descriptions. The program is ambitious and opens up on many possibilities of experimental, observational and theoretical developments in physics as well as in interdisciplinary fields as already illustrated in a number of recent publications inscribing the fundamental results outlined in this review in more general approaches [7,8,11] or applying them to problems in fields as varied as fundamental physics [24,4], cosmology [12], atomic physics [14], material science [41], or biology [42].…”

Editorial: Analytical methods for nonlinear oscillators and solitary waves

“…Fractal soliton, on the other hand, is a solitary wave moving along an unsmooth boundary or through a porous medium [1]. When an attosecond electron beam is trapped in and propagate with the laser pulse, the travelling solitary wave can be modelled in a fractal space [2], and the attosecond physics won 2023 Nobel Prize in Physics [3]. Discontinuous time appears on an attosecond (10 −18 s) scale, so fractal time has to be adopted [4,5], and pinpointing the fractal dimensions is tricky, especially when the studied system has not seeming self-similarity, now He-Liu's fractal dimensions formulation [6] makes the fractal theory accessible to porous media and discontinuous time.…”

Coulomb-Corrected Strong Field Approximation without Singularities and Branching Points

“…Since the SFA does not offer a proper explanation of various experimental results, it requires further developments. For instance, an attempt to incorporate the interaction of photoelectrons with the parent ion by means of the Coulomb-Volkov state was undertaken in [15][16][17]. This procedure was successfully applied to the analysis of ionization driven by elliptically polarized laser fields [18].…”

“…Subsequently, such approximation has been extended to treat the non-relativistic laser-assisted scattering processes [10] and its relativistic counterpart [11], where the relativistic form of the Volkov solution [12-14] is fully exploited.Since the SFA does not offer a proper explanation of various experimental results, it requires further developments. For instance, an attempt to incorporate the interaction of photoelectrons with the parent ion by means of the Coulomb-Volkov state was undertaken in [15][16][17]. This procedure was successfully applied to the analysis of ionization driven by elliptically polarized laser fields [18].…”