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Saratov Fall Meeting: Laser Physics, Photonic Technologies, and Molecular Modeling

One-dimensional "atom" with zero-range potential perturbed by finite sequence of zero-duration laser pulses

Vladimir Leonardovich Derbov, Alexander A. Gusev, Ochbadrakh Chuluunbaatar, Sergue Il'ich Vinitsky, Yuri V. Popov, Konstantin P. Lovetskiy

Published Apr 26, 2018• 0 citations
Publisher

Abstract

The exactly soluble model of a train of zero-duration electromagnetic pulses interacting with a 1D atom with short-range interaction potential modelled by a δ-function is considered. The model is related to the up-to-date laser techniques providing the duration of pulses as short as a few attoseconds and the intensities higher than 1014 W/cm2.

DOI
10.1117/12.2315880

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The exactly soluble model of a train of zero-duration electromagnetic pulses interacting with a 1D atom with short-range interaction potential modelled by a δ-function is considered. The model is related to the up-to-date laser techniques providing the duration of pulses as short as a few attoseconds and the intensities higher than 1014 W/cm2.
We have developed a theory of the one-dimensional atomic trap formed by the resonant counterpropagating trains of the short small-area laser pulses. Atoms are trapped in the region where the counterpropagating pulses 'collide'. We have derived the effective Hamiltonian which allows us to consider an atom in the polychromatic field of the pulse trains as the atom with the spatially modulated transition frequency in a standing monochromatic wave. We have obtained the expressions for the coordinate-dependent force exerted on the atom and the atom potential energy. The value of the potential barrier for typical femtosecond laser parameters for an atom with mass ~100 amu is approximately 15 mK.
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.
We study the time evolution of the wave function of a particle bound by an attractive δ-function potential when it is subjected to time-dependent variations of the binding strength (parametric excitation). The simplicity of this model permits certain nonperturbative calculations to be carried out analytically both in one and three dimensions. Thus the survival probability of bound state |θ(t)|2, following a pulse of strength r and duration t, behaves as |θ(t)|2−|θ(∞)|2∼t−α, with both θ(∞) and α depending on r. On the other hand, a sequence of short pulses produces an exponential decay over an intermediate time scale.
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.