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Physical Review A

Interaction of multilevel atoms with classical time-dependent fields

G. W. F. Drake, R. B. Grimley

Published May 1, 1975• 20 citations
Publisher

Abstract

A wide class of problems is considered involving the interaction of multilevel atoms with classical time-dependent fields switched on at a definite time. It is shown that the exact time-dependent Green's function can be written as the particular solution to an inhomogeneous differential equation involving derivatives with respect to the external field variables. Asymptotic expansions are discussed and analytic solutions found for several cases. The time and frequency distributions of radiation emitted by a field-perturbed atom are calculated by including the radiation field as a first-order perturbation.

DOI
10.1103/physreva.11.1614

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A wide class of problems is considered involving the interaction of multilevel atoms with classical time-dependent fields switched on at a definite time. It is shown that the exact time-dependent Green's function can be written as the particular solution to an inhomogeneous differential equation involving derivatives with respect to the external field variables. Asymptotic expansions are discussed and analytic solutions found for several cases. The time and frequency distributions of radiation emitted by a field-perturbed atom are calculated by including the radiation field as a first-order perturbation.
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We consider the radiation from a system of NNN identical two-level atoms coupled to a continuum of quantized em modes, and possibly, to an external driving field near resonance. The atoms can be distributed over a region large in comparison to the resonant wavelength, but smaller than the spontaneous pulse length. Radiation rates and correlation functions are expressed in terms of expectation values of time-dependent atomic operators, which are shown to satisfy coupled first-order differential equations involving similar atomic operators and the initial radiation operators. The corresponding equations for the expectation values simplify considerably if no driving field is present. Similar results are derived for a model in which each atom is replaced by a harmonic oscillator.
In the framework of an exactly soluble model, one considers a typical problem of the interaction between radiation and matter: the dynamics of population in a multilevel quantum system subject to a time dependent perturbation. The algebraic structure of the model is taken richly enough, such that there exists a strong argument in favor of the fact that the behavior of the system in the asymptotic of long time has a universal character, which is system-independent and governed by the functional property of the time dependence exclusively. Functional properties of the excitation time dependence, resulting in the regimes of resonant excitation, random walks, and dynamic localization, are identified. Moreover, an intermediate regime between the random walks and the localization is identified for the polyharmonic excitation at frequencies given by the Liouville numbers.
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We develop the group-theoretical approach for analytically solving the time-dependent Schrodinger equations for multilevel atoms driven by amplitude- and/or frequency-modulated concurrent laser fields. The time evolution of externally driven N-level atoms is calculated in an explicit matrix form. The exact analytical conditions for complete population transfer and its return are simply connected with the parameters of the symmetry. We consider in detail the case of a four-level system driven by concurrent laser pulses of different forms.
In describing the nonlinear interaction of radiation with matter it is well known that the perturbation expansion technique is used to calculate the atomic wave functions and the transitions between the states of a system. However the technique, though involving all states of the system, is valid only in the limit of weak interaction fields and non-resonant interactions. For strong fields and resonant interactions, density matrix or dressed atom formulisms are commonly used though these exact treatments are restricted to simple two level schemes or approximations of these; their application to general resonant-near resonant multilevel interactions being prohibitively complex.