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Physics-Uspekhi

Simple atomic systems in resonant laser fields

Mikhail L. Ter-Mikhaelyan

Published Dec 31, 1997• 42 citations
Publisher

Abstract

The interaction of simple, two- and three-level atomic systems with monochromatic and nonmonochromatic laser radiation near resonance transitions is discussed based on the Schroedinger equation with radiation decay and no collisional relaxation, outside the framework of the usual perturbation theory. The mathematical schemes employed include the resonance approximation, exact methods, the quasi-energy method, the adiabatic approximation, etc. A large number of physical phenomena, such as oscillating and inverted populations, self-induced resonances, processes of first order in the weak field, Raman scattering, coherent population transfer, etc. are considered. The review is intended for a broad readership.

DOI
10.1070/pu1997v040n12abeh000318

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The interaction of simple, two- and three-level atomic systems with monochromatic and nonmonochromatic laser radiation near resonance transitions is discussed based on the Schroedinger equation with radiation decay and no collisional relaxation, outside the framework of the usual perturbation theory. The mathematical schemes employed include the resonance approximation, exact methods, the quasi-energy method, the adiabatic approximation, etc. A large number of physical phenomena, such as oscillating and inverted populations, self-induced resonances, processes of first order in the weak field, Raman scattering, coherent population transfer, etc. are considered. The review is intended for a broad readership.
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The problem of a two-level atom interacting with a non-monochromatic radiation pulse is studied in the resonant approximation for arbitrary detunings, and without the resonant approximation. By using the time-dependent theory of perturbation the analytical expressions for the transition probability and induced dipole moment of the atom are obtained. It is shown that the upper level population of the atom exhibits oscillations that are absent in the resonant approximation. The temporal shape of the pulse is shown to affect significantly the atomic transition probability. The behaviour of the transition probability and dipole moment spectrum for arbitrary pulse shapes, phases and detunings is investigated. The interference between the spectral components arising in nonlinear processes is shown to play a considerable role in the formation of a dipole moment spectrum.
We study numerically the solution to Schr\"odinger's equation for the radiative interaction of fictitious NNN-level model atomic and molecular systems with monochromatic radiation fields. The numerical method of solution allows us to study multiphoton transitions in NNN-level systems unhampered by the assumptions usually adopted, such as weak fields or large detunings of intermediate states, in perturbative and quasiperturbative analytic studies. We point out regularities and near regularities in the population dynamics that appear to be qualitatively different from those encountered in two- and three-level systems.
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Coherent manipulations of atoms using laser light The internal structure of a particle - an atom or other quantum system in which the excitation energies are discrete - undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space statevector that provides the theoretical portrait of probability amplitudes - the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laser-pulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a three-dimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping "dark" states.
Results are reported on coherent monochromatic multiphoton excitation in many-level systems, which are representative for some of the basic mechanisms for atomic and molecular multiphoton processes. Numerical solutions are discussed that use the Floquet and quasi-resonant approximations in the framework of the URIMIR program package. The excitation schemes include direct three-photon excitation, two-photon excitation with diagonal coupling, Göppert-Mayer-type two-photon processes, multiphoton excitation with off-resonant inter-mediates, and practically irreversible coherent excitation into dense spectral structures. Several interesting phenomena are observed, such as nonlinear line shifts and broadenings of multi-photon resonances of relevance for multiphoton spectroscopy and almost constant intermediate population inversions, potentially useful for laser design. The accurate numerical results are compared with approximate solutions from perturbation theory, and with simple analytical solutions from Rabi-type formulae.