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Journal of Physics Conference Series

“Middle way” in the description of ultrashort electromagnetic interactions: between Fermi’s golden rule and the numerical solution of the Schrödinger equation

Valery Alexandrovich Astapenko, Egor Sergeevich Khramov, Timur Bergaliyev

Published Feb 1, 2024• 3 citations

Abstract

Abstract A simple efficient approach describing the interaction of various quantum targets with short electromagnetic (EM) pulses firstly proposed in [1] is reviewed. This approach is based on the expression for the photoprocess probability in terms of the cross section and the Fourier transform of the EM pulse. Our method makes it possible to take into account the internal dynamics of the target and the influence of the pulse parameters in a simple way. The proposed approach is used both for the probability for the entire pulse duration, and for its dependence on the current time. In addition, the developed method is applied to generalize the simulation of the population kinetics of a quantum system to take into account the dependence of the photoprocess rate on time. It is also shown that our expression for the probability of excitation of a micro-target corresponds to the formula describing the energy loss of a non-monochromatic field in a dispersive medium and can be generalized on other EM processes.

DOI: 10.1088/1742-6596/2701/1/012092

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Abstract The time dependence (on the pulse duration and on current time) of resonant photoprocesses induced by electromagnetic pulses of various durations (including ultrashort and quasi-monochromatic pulses) is analyzed using perturbation theory. Pulses with the Gaussian and exponential envelopes, as well as the Lorentzian and Gaussian spectral profiles of a photoprocess cross section are considered. Simple analytic expressions are obtained for the probability in the long-time limit. The time dependence for a given pulse duration is investigated analytically in the monochromatic and ultrashort limits and numerically for intermediate values of parameters. Specific features of the temporal dynamics, which are common for resonant photoprocesses and depend on the pulse shape and the spectral cross section profile are established.

The development of methods of generation of ultrashort pulses (USP) of femto- and attosecond duration ranges with controlled parameters necessitates the theoretical study of features of their interaction with a matter [1]. Among such features that do not exist in case of “long” pulses should first of all be the nonlinear dependence of the photoprocess probability W on the USP duration (τ) [2] as well as the dependence on the carrier phase with respect to the pulse envelope (φ) [3-4]. It should be noted that if the dependence of the probability W on the phase φ manifests itself either only for very short pulses, when ωτ < 1 (ω is carrier frequency of the pulse), or in case of a nonlinear photoprocess [3], the function W(τ) can differ from a linear function in the limit ωτ> 1 too for fields of moderate strength, when the perturbation theory is applicable [2].

Electron transitions and emission of an atom interacting with a spatially inhomogeneous ultrashort electromagnetic pulse are considered. The excitation and ionization probabilities are obtained as well as the spectra and cross sections of the reemission of such a pulse by atoms. By way of an example, one-and two-electron inelastic processes accompanying the interaction of ultrashort pulses with hydrogen-and helium-like atoms are considered. The developed technique makes it possible to take into account exactly the spatial non-uniformity of the ultrashort pulse field and photon momenta in the course of reemission.

Inelastic processes and the reemission of attosecond and shorter electromagnetic pulses by atoms have been considered within the analytical solution of the Schrödinger equation in the sudden perturbation approximation. A method of calculations with the exact inclusion of spatial inhomogeneity of the field of an ultrashort pulse and the momenta of photons in the reemission processes has been developed. The probabilities of inelastic processes and spectra of reemission of ultrashort electromagnetic pulses by one- and many-electron atoms have been calculated. The results have been presented in the form of analytical formulas.

The development of methods of generation of ultrashort pulses (USP) of femto- and attosecond duration ranges with controlled parameters necessitates the theoretical study of features of their interaction with a matter. Among such features that do not exist in case of “long” pulses should first of all be the nonlinear dependence of the photoprocess probability W on the USP duration as well as the dependence on the carrier phase with respect to the pulse envelope. It should be noted that if the dependence of the probability W on the phase manifests itself either only for very short pulses, when ωt 1 too for fields of moderate strength, when the perturbation theory is applicable. The present work is dedicated to the theoretical analysis of two-photon excitation of hydrogen atom in a discrete energy spectrum by ultrashort electromagnetic pulses of femto- and subfemtosecond ranges of durations. As examples, excitation of hydrogen atom from the ground state to excited states with a zero orbital moment is considered.

Abstract The dynamics of time evolution of quantum oscillator excitation by electromagnetic pulses is investigated theoretically for an arbitrary field amplitude in a pulse. We consider a harmonic oscillator without damping and excitation between stationary states. The general formula for the excitation of quantum states as a function of time is derived in terms of instantaneous energy of an associated classical oscillator in the field of an electromagnetic pulse. The derived expression is used in detailed analysis of the time dependence of the quantum oscillator excitation probability beyond the range of perturbation theory for various pulse parameters including total excitation from the ground state, excitation from excited states, and excitation spectra.