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Journal of Modern Optics

Rates and Recurrences in Quasicontinuum Photoexcitation

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

Published May 1, 1987• 15 citations
Publisher

Abstract

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.

DOI
10.1080/09500348714550621

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Physical Review A•Aug 1, 1998•6 citations
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 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.
We consider the process of photoassociation (PA) that occurs when a pair of colliding atoms interacts with a photon, thereby making a transition from the two-atom continuum to a bound molecular state. Such free-bound transitions are described by quantizing the molecule's dissociation continuum, and coupling each of these quasicontinuum (QC) levels to a similarly discrete molecular level. The correct free-atom results are recovered no later than at the end of a given calculation by taking the limit as the QC spacing tends to zero. From the quasicontinuum model, we are led to adapt the few-level and second-quantization methods of photon optics to analyze free-bound transitions. In particular, we establish the PA density parameter as nearly identical to the phase-space parameter as a Bose-Einstein condensate (BEC), illustrate the near-unit efficiency of one- and two-color photoassociation of a BEC, and develop coherent atom-molecule transitions as the matter optics version of second-harmonic generated photons. ^
We use a semlclassical, effective-state approach to laser pulse propagation in a gas of polyatomic molecules. Our numerical model of multiple-photon excitation includes quasicontinuum transitions to calculate the effects of coherent propagation on multiple- photon absorption. The molecular model consists of a single ground state and several bands of discrete states, which are successively connected by means of electric-dipole transitions.1 This model correctly simulates some of the major characteristics of multiple- photon absorption, such as power threshold, fluence-dependent absorption, and complete population inversion at large fluences. As the pulse propagates, the Rabi oscillations induced in the lower-level states are encoded onto the pulse and create a series of peaks and troughs similar to those found in pulse propagation in two-level systems.2 Another coherent propagation effect that can change the excitation process is coherent sideband generation. Temporal distortions and the generation of new frequencies result in changes in the population distribution among the states, as well as changes in the total population transferred to the quasicontinuum. The effective increase in total population transfer by propagation effects is offset by the decrease in fluence. The resulting transfer of energy from the pulse to the molecule depends strongly on the initial characteristics of the pulse.
In this thesis I present several theoretical methods to explore the excitation dynamics of Ultracold Rydberg systems in various regimes. For some applications the details of interactions between Rydberg atoms have to be carefully examined, while for others, the many-body aspect of Rydberg excitation may be crucial. In both cases, the basic prerequisite is to know the interactions sufficiently well. I will review the basic concepts how to evaluate molecular potentials in various Hund's cases and approximations. Long-range Rydberg-Rydberg interactions between Rydberg atoms induce ℓ-mixing which in certain situations gives rise to molecular resonances. For these resonances, we calculate long-range potentials in Hund's case (c) by diagonalization of an interaction matrix. The excitation dynamics of the resonances is always modeled as pair excitation. At high principal quantum number n, the interactions between Rydberg atoms can blockade the excitation of many surrounding atoms in the range of few μm. The atoms within this range are strongly correlated so that many-body treatments are, in general, needed. To describe this blockading effect and other manifestations of the collective behavior of Rydberg excitation, such as the many-body Rabi oscillations, spatial correlations between atoms and the fluctuations of the number of excited atoms, I have used three different approaches. In the mean-field approach the interactions between different atoms is modeled by a distribution of mean-field shifts for which a distribution of probabilities is calculated, A good agreement between the theoretical model and experimental measurements is found. To study the correlations between atoms the many-body wavefunction is numerically computed. The possibility of observing the many-body Rabi oscillations of Rydberg excitation and other aspects of many-body dynamics is analyzed. Although strong interactions cannot be treated perturbatively other expansions may be feasible. I will show that the expansion in powers of the single atom Rabi frequency can be evaluated in the interaction and Heisenberg picture. The expansion is expected to behave well for arbitrary strong interactions. ^
Three distinct phenomena are found to affect the autoionization of a quasicontinuum. For certain initial superpositions of the states within the quasicontinuum, the autoionization may be inhibited by quantum interference and the population may be trapped. For those initial superpositions that do decay, a self-trapping effect can be observed which causes the superposition to evolve into a trapped state. The self-trapping is due to a redistribution of the population within the quasicontinuum via Raman-like transitions driven by the channel interaction with the continuum acting as the intermediate state. The physical system of a two-electron atom is studied. There the autoionizing continuum is created by an isolated core excitation that embeds a range of highly excited Rydberg states into the continuum. Another mechanism appears, in this system, that affects the autoionization. When the channel interaction is strong compared to the strength of the core excitation a stabilizing effect occurs which slows the autoionization. Analytical models examine these effects in a system with degenerate quasicontinua. Perfect population trapping, self-trapping, and stabilization are all clearly displayed by this system. Numerical models of nondegenerate quasicontinua show that the stabilization process is virtually unchanged by the lifting of the degeneracy. These models also show that, in general, the trapping effects largely disappear. However, a synchronization of the free evolution of the quasicontinuum states with Rabi oscillation of the core excitation returns them to significant roles in the decay process. A wide variety of nondecaying states can be created. Competition between these mechanisms is explored and the impact of these phenomena on experiments is considered.