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Journal of Modern Optics

Photoexcitation to a Periodic Continuum

PAUL M. RADMORE

Published Mar 1, 1995• 5 citations
Publisher

Abstract

It is shown that, under rather general conditions, a single discrete (ground) state being excited to a continuum with periodic structure will experience a periodic disruption in the time-evolution of its population and that, in the initial interval before the first disruption, this evolution always follows that of the Weisskopf-Wigner result. A general formula for the ground-state amplitude is found in terms of the Fourier coefficients of the coupling, and special cases are considered.

DOI
10.1080/09500349514550541

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It is shown that, under rather general conditions, a single discrete (ground) state being excited to a continuum with periodic structure will experience a periodic disruption in the time-evolution of its population and that, in the initial interval before the first disruption, this evolution always follows that of the Weisskopf-Wigner result. A general formula for the ground-state amplitude is found in terms of the Fourier coefficients of the coupling, and special cases are considered.
The photoexcitation of a structured continuum of states from a single ground state is considered. We investigate an analytically soluble model in which the dipole matrix elements between the ground state and the continuum vary sinusoidally between zero and a maximum. The time-evolution of the ground-state population still exhibits the periodic disruption observed in the Bixon-Jortner model, although the disruption is much reduced. We allow the ground state to be resonant with an arbitrary place in the continuum; population trapping is observed in the case of resonance with a zero in the continuum. We compare and contrast the results obtained with this model with those of quasi-continuum excitation. Lastly, we examine the final-state spectrum.
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 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.
We consider the effect of a field with time-varying phase on the final-state spectrum produced by ionization of a single ground-state. Although the ground-state population still decays according to the Weisskopf-Wigner formula, the final-state spectrum exhibits a redistribution of population. A single Lorentzian is, in general, no longer obtained and the spectrum may be asymmetric. We concentrate on analytically soluble models with periodic phase-variation, but also briefly consider a random phase and chirp. Finally, the case of two continua is discussed.
Studies the coupling of N discrete levels to a common continuum. The discrete levels, which can include both genuine bound states and autoionisation states, are assumed to be coupled to the continuum and to each other in such a way as to permit a rotating wave approximation in the Schrodinger equation. A general solution for the model is derived with the aid of Laplace transforms and the Weisskopf-Wigner approximation. The author discusses general properties of the discrete level populations and the electron spectrum like population trapping, zeros, crossings, resonances and confluences. As examples the author treats cases where two or three discrete levels interact with a continuum.
In this paper we analyze the dynamics of single-excitation states, which model the scattering of a single photon from multiple two level atoms. For short times and weak atom-field couplings we show that the atomic amplitudes are given by a sum of decaying exponentials, where the decay rates and Lamb shifts are given by the poles of a certain analytic function. This result is a refinement of the "pole approximation" appearing in the standard Wigner-Weisskopf analysis of spontaneous emission. On the other hand, at large times, the atomic field decays like O(1/t3)O(1/t^3)O(1/t3) with a known constant expressed in terms of the coupling parameter and the resonant frequency of the atoms. Moreover, we show that for stronger coupling, the solutions also feature a collection of oscillatory exponentials which dominate the behavior at long times. Finally, we extend the analysis to the continuum limit in which atoms are distributed according to a given density.