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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.
In dense atomic gases the interaction between transition dipoles and photons leads to the formation of many-body states with collective dissipation and long-ranged forces. Despite decades of research, a full understanding of this paradigmatic many-bo
Photoelectron emission from excited states of laser-dressed atomic helium is analyzed with respect to laser intensity-dependent excitation energy shifts and angular distributions. In the two-color XUV (exteme ultra-violet) -- IR (infrared) measuremen
We theoretically study trapped ions that are immersed in an ultracold gas of Rydberg-dressed atoms. By off-resonant coupling on a dipole-forbidden transition, the adiabatic atom-ion potential can be made repulsive. We study the energy exchange betwee
We describe numerically the ionization process induced by linearly and circularly polarized XUV attosecond laser pulses on an aligned atomic target, specifically, the excited state Ne$^*(1s^22s^22p^5[{}^2text{P}^text{o}_{1/2}]3s[^1text{P}^o])$. We co
We analyse a system composed of a qubit coupled to electromagnetic fields of two high quality quantum oscillators. Particular realization of such a system is the superconducting qubit coupled to a transmission-line resonator driven by two signals wit