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Physical Review A

Dressed states and spectra in quasicontinuum excitation

Sam Tarzi, PAUL M. RADMORE

Published Jun 1, 1988• 7 citations
Publisher

Abstract

We consider a system in which a ground state is coupled to a general quasicontinuum of levels and to a true continuum. In the long-time limit, the true continuum spectrum can exhibit zeros, the positions of which depend on the energies of the quasicontinuum levels. The initial conditions determine the existence of these zeros. We describe this phenomenon by studying dressed states for the complete system and in particular derive dressed states which are ground-state independent. We use these to explain the locations of the zeros and their dependence on the initial conditions.

DOI
10.1103/physreva.37.4734

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We consider a system in which a ground state is coupled to a general quasicontinuum of levels and to a true continuum. In the long-time limit, the true continuum spectrum can exhibit zeros, the positions of which depend on the energies of the quasicontinuum levels. The initial conditions determine the existence of these zeros. We describe this phenomenon by studying dressed states for the complete system and in particular derive dressed states which are ground-state independent. We use these to explain the locations of the zeros and their dependence on the initial conditions.
We examine the excitation of continuum-state resonances close to the threshold, paying particular attention to the breakdown of the Markov approximation and the consequences of this for initial-state time dependences and final-state spectra. Several theoretical dressed-state alternative descriptions are analyzed and compared: the nonperturbative coupling of a discrete state to a structured continuum with a threshold, the complete Fano diagonalization of the interacting system, and finally a partial diagonalization of the bound-state couplings to reveal the origin of dressed-state stabilization and partial decay suppression observed in this model.
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.
An isolated level coupled to a continuum of levels need not decay fully into them. Ordinarily one expects exponential decay, module finite-size effects, transients and long-time power-law tails. In the phenomenon we describe the amplitude for remaining in the initial state at first drops, but it then levels off and remains O(1) indefinitely. Because of the available continuum, this is different from certain quantum localization phenomena where there is an absence of on-shell levels. The origin of the effect we describe is the existence of thresholds and band edges. A condition relating the proximity to threshold with the strength of the coupling determines whether the limited decay occurs.
We present an analytical solution to a multilevel model of light-induced continuum structure, in which, instead of a single level, a quasicontinuum of excited levels is laser embedded into a previously structureless atomic continuum. The found solution is fully time dependent and is valid for probing strengths of the structured continuum from the ground level by another laser, which can vary from being much weaker than the embedding one to being as strong as the embedding one. For three different embeddings (weak, moderate, and strong), each one determined by a different relation between the ionization rate \ensuremath{\gamma} and the spacing \ensuremath{\Delta} of the quasicontinuum levels (\ensuremath{\Elzxh}\ensuremath{\gamma}/\ensuremath{\Delta}\ensuremath{\ll}1, \ensuremath{\Elzxh}\ensuremath{\gamma}/\ensuremath{\Delta}\ensuremath{\simeq}1, and \ensuremath{\Elzxh}\ensuremath{\gamma}/\ensuremath{\Delta}\ensuremath{\gg}1), we study the evolution of the ionization spectrum with increasing probing strength. We observe and interpret such strong-field effects in the spectra as (i) conversion of a Fano-like train of peaks into a train of dips; (ii) peak moving, narrowing, and lowering; and (iii) saturation, population trapping, and stabilization against ionization.
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.