Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Photoexcitation of a quasi-continuum: connections to few-level dynamics

Erkki Kyrola

Published Oct 1, 1984• 14 citations
Publisher

Abstract

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.

DOI
10.1364/josab.1.000737

Related papers

Rates and Recurrences in Quasicontinuum Photoexcitation

PAUL M. RADMORE, Sam Tarzi, P. L. Knight

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.

Journal of Modern Optics•May 1, 1987•15 citations

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

Erkki Kyrola

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.

Journal of the Optical Society of America B•Mar 1, 1986•7 citations

Quasicontinuum effects in molecular excitation

Erkki Kyrola, Joseph H. Eberly

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.

The Journal of Chemical Physics•Feb 15, 1985•46 citations

Photoexcitation to a Periodic Continuum

PAUL M. RADMORE

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.

Journal of Modern Optics•Mar 1, 1995•5 citations

Nonexponential decay via tunneling to a continuum of finite width

Eugene Kogan

A simple quantum mechanical model consisting of a discrete level resonantly coupled to a continuum of finite width, where the coupling can be varied from perturbative to strong, is considered. The particle is initially localized at the discrete level, and the time dependence of the amplitude to find the particle at the discrete level is calculated without resorting to perturbation theory and using only elementary methods. A simple and convenient, both for qualitative analysis and for numerical calculations, formula for the amplitude as a function of time is obtained.

arXiv:quant-ph/0611043•Jan 1, 2007•0 citations

Analysis of single-excitation states in quantum optics

Jeremy G. Hoskins, Jason Kaye, Manas Rachh +1 more

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 $O(1/t^3)$ 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.

arXiv:2110.07049•Oct 13, 2021•0 citations
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 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 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.
A simple quantum mechanical model consisting of a discrete level resonantly coupled to a continuum of finite width, where the coupling can be varied from perturbative to strong, is considered. The particle is initially localized at the discrete level, and the time dependence of the amplitude to find the particle at the discrete level is calculated without resorting to perturbation theory and using only elementary methods. A simple and convenient, both for qualitative analysis and for numerical calculations, formula for the amplitude as a function of time is obtained.
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.