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Journal of the Optical Society of America B

Sudden and adiabatic approximations in the excitation of a quasi-continuum

Erkki Kyrola

Published Mar 1, 1986• 7 citations
Publisher

Abstract

We study the coupling of a single initially occupied level to a quasi-continuum (QC) by a smoothly switched field. In the weak-field limit the dynamics is solved for an infinite, uniform, and flat QC by using perturbation theory. For a field switched on well before the recurrence time of the QC we find the peculiar ratelike time development of the sudden approximation with small modifications. For a slower turn-on we obtain an adiabatic excitation of the QC levels accompanied by quadratic and periodic oscillations of the initial state population. In the strong-field limit we find that the population recurrences of the sudden approximation gradually disappear when the turn-on time is increased. In the very-strong-field limit we demonstrate that this leads to the possibility of the adiabatic population inversion.

DOI
10.1364/josab.3.000453

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We study the coupling of a single initially occupied level to a quasi-continuum (QC) by a smoothly switched field. In the weak-field limit the dynamics is solved for an infinite, uniform, and flat QC by using perturbation theory. For a field switched on well before the recurrence time of the QC we find the peculiar ratelike time development of the sudden approximation with small modifications. For a slower turn-on we obtain an adiabatic excitation of the QC levels accompanied by quadratic and periodic oscillations of the initial state population. In the strong-field limit we find that the population recurrences of the sudden approximation gradually disappear when the turn-on time is increased. In the very-strong-field limit we demonstrate that this leads to the possibility of the adiabatic population inversion.
We study the coupling of an initially occupied single level to an N-level quasi-continuum (QC) using perturbation theory. The single-level amplitude is expressed as a sum of harmonically oscillating factors whose dephasings and rephasings give rise to decay and recurrences, respectively. In particular, we study the most common model of this coupling in which the QC is infinite, uniform, and flat. We derive simple approximate formulas for resonant and nonresonant excitation that display absorption-rate reversal and enhancement effects and periodic time evolution. We show how these properties can be connected to few-level dynamics. The limits of applicability of few-level approximations are investigated.
The photoexcitation of a quasicontinuum of atomic or molecular levels by a laser pulse with a fast rise-time is considered. We first generalize non-perturbative treatments of quasicontinuum excitation. A second general theoretical method is developed in which resonant states are considered non-perturbatively whereas background non-resonant states are included through a perturbative approximation. As a simple example we show how our method describes the photoexcitation of a quasicontinuum of equally spaced levels, exhibiting Rabi oscillations periodically perturbed by background states. We then examine the case of a Rydberg series of highly excited states coherently excited from a low-lying initial state. The time evolution of the coherent superposition of Rydberg levels is shown to be a perturbed Rabi oscillation, but without the periodic disruption of the equally spaced quasicontinuum. Finally, we include the effect of further excitation to a second continuum.
We study a model where two discrete levels are coupled to a band of closely spaced levels forming a quasicontinuum (QC). This model describes how the initial-stage coherence in multiphoton excitation of polyatomic molecules interferes with the recurrent time dynamics due to the QC coupling. The time evolution of the system is solved exactly assuming the QC to be infinite, flat, and uniform; and a detailed investigation of different special cases is carried out. Weak QC excitation is found to exhibit features which are connected to few level dynamics rather than to an irreversible decay, and we study how this modifies the absorption cross section and the Rabi oscillations. The conditions for coherent trapping are discussed.
Abstract The population transfer dynamics in a strongly driven two-level system is studied. It is shown that population inversion can be efficiently achieved when a laser pulse whose photon energy is about half of the energy separation of the two levels is turned on suddenly. This situation is realized when a neutral atom or molecule is ionized at the peak of the laser field, followed by the laser-driven population transfer among two states of an atomic or molecular ion. The mechanism of the efficient population transfer for an ion effectively exposed to a laser field with a sudden turn-on is examined by numerical calculations based on the quasi-stationary Floquet theory.
We present a fully quantum-mechanical theory of the mutual light-matter effects when two laser pulses interact with three discrete states coupled to a (quasi)continuum. Our formulation uses a single set of equations to describe the time dependence of the discrete and continuum populations, as well as pulse propagation in electromagnetically induced transparency (EIT) and stimulated Raman adiabatic passage (STIRAP) situations, for both weak and strong laser pulses. The theory gives a mechanistic picture of the ``slowing down of light'' and the state of spontaneously emitted photons during this process. Surprising features regarding the time dependence of material and radiative transients as well as limitations on quantum light storage and retrieval are unraveled.