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Physical Review A

Near-threshold excitation of continuum resonances

B. Piraux, R. N. Bhatt, P. L. Knight

Published Jun 1, 1990• 42 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.41.6296

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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.
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Near-threshold single-photon photodetachment processes are considered for simple model systems representing negative ions exposed to monochromatic radiation. The model systems considered feature an initial discrete state, the photoelectron continuum, and in some cases an excited or autodetaching discrete state. Population trapping through the formation of a bound dressed state and the photoelectron spectra are examined. Two photoelectron spectra are defined : a primary spectrum which results from decay while the laser interaction is on and a secondary spectrum which results from the destabilization of the bound dressed state if the interaction is turned off again. Careful attention is given to the passage of the poles of the Green's operator through the low-energy boundary of a continuum, and it is concluded that such poles move nonmonotonically through the boundary of an s-wave continuum, but monotonically through the boundary of a p-wave or higher-l-wave continuum. Two example systems, one featuring a single discrete state and an s-wave continuum and one featuring two discrete states and a p-wave continuum, are considered in detail.
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.
Fano resonance is a well-celebrated weak-coupling phenomenon whereby a small interaction between a discrete and a continuum of excited states leads to an interference between the respective two transition amplitudes, resulting in an asymmetric line shape in the excitation spectra. We present the strong-coupling phase of the Fano's model where the interaction is localized in a region $\ensuremath{\xi}$ that is smaller than the collective coupling between the discrete state and the continuum. We explore the behavior of the excitation probability $\ensuremath{\sigma}$ as a function of $\ensuremath{\xi}$, the ratio of the bare transition amplitudes, and the energy of the discrete state. In the strong-coupling phase, the spectral function of the discrete state splits up and produces up to three complete destructive interferences or zeros of $\ensuremath{\sigma}$ along with ultrasharp features. We also find that the discrete state does not have to lie within the continuum to produce the well-known weak-coupling profiles of $\ensuremath{\sigma}$ as long as the collective coupling is strong enough. In addition, we consider a broadened state instead of a continuum and present a method that exactly treats such cases by explicitly including the source of the broadening---a weak coupling to the continuum of environment states---in the model.
The eigenvalue problem for the dressed bound state of unstable multilevel systems is examined both outside and inside the continuum, based on the NNN-level Friedrichs model, which describes the couplings between the discrete levels and the continuous spectrum. It is shown that a bound-state eigenenergy always exists below each of the discrete levels that lie outside the continuum. Furthermore, by strengthening the couplings gradually, the eigenenergy corresponding to each of the discrete levels inside the continuum finally emerges. On the other hand, the absence of the eigenenergy inside the continuum is proved in weak but finite coupling regimes, provided that each of the form factors that determine the transition between some definite level and the continuum does not vanish at that energy level. An application to the spontaneous emission process for the hydrogen atom interacting with the electromagnetic field is demonstrated.
The effects of saturation of a bound-bound atomic resonance on bound-continuum decays in investigated using the dressed state concept. Two special cases are discussed: the modification of spontaneous radiative decay by coupling to a third bound atomic state, and the changes in single-photon photoionisation when the initial discrete state is coupled by an external field to another bound state. For strong external fields Rabi oscillations and dynamic Stark splittings profoundly alter the 'decay'; but for weak fields the alterations at line centre are no less dramatic.