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Physical Review A

Radiative decay of autoionizing states in laser fields. I. General theory

G. S. Agarwal, Stanley L. Haan, J. Cooper

Published May 1, 1984• 77 citations
Publisher

Abstract

A theory describing the radiative decay of an autoionizing state under strong pumping by a coherent field is developed. The theory systematically takes into account the radiative decay of the unperturbed continuum. The problem at hand corresponds to the case of strongly coupled bound states decaying to electron and photon continua with the two continua also weakly coupled to each other. A master equation describing the time evolution of the atomic system is derived, and its exact solution under arbitrary initial conditions is given. The effect of radiative decay on the Fano profiles and photoelectron spectra is analyzed in detail. The time development of the system is also examined. The radiative decay of the autoionizing state and the unperturbed continuum changes the spectra in a significant way. The characteristics of the spectra are correlated with the dressed states (with complex energies) of the system. The changes in the structure of the dressed states as a function of the system parameters such as the spontaneous-emission rate and laser intensity are discussed in detail.

DOI
10.1103/physreva.29.2552

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A theory describing the radiative decay of an autoionizing state under strong pumping by a coherent field is developed. The theory systematically takes into account the radiative decay of the unperturbed continuum. The problem at hand corresponds to the case of strongly coupled bound states decaying to electron and photon continua with the two continua also weakly coupled to each other. A master equation describing the time evolution of the atomic system is derived, and its exact solution under arbitrary initial conditions is given. The effect of radiative decay on the Fano profiles and photoelectron spectra is analyzed in detail. The time development of the system is also examined. The radiative decay of the autoionizing state and the unperturbed continuum changes the spectra in a significant way. The characteristics of the spectra are correlated with the dressed states (with complex energies) of the system. The changes in the structure of the dressed states as a function of the system parameters such as the spontaneous-emission rate and laser intensity are discussed in detail.
Complex dressed states and photoelectron spectra are considered for a model system containing two discrete states that are coupled by separate lasers to a continuum that supports a resonance such as an autoionizing state. Spontaneous radiative decay from the structured continuum has been included and its effects are examined. It is shown that population can be trapped within the model atom even when radiative decay is included provided (1) the two Fano q values which characterize the discrete-state--continuum interactions are equal, and (2) the two-photon resonance condition is satisfied.
The fluorescence produced by an autoionizing state under strong pumping by a coherent laser field is considered. It is shown how the spectrum of emitted photons and the total number of photons are related to the two-time and single-time atomic expectation values, and explicit expressions are derived for them. Numerical results for the time development of the number of photons ejected are presented for finite times and in the long-time limit. The photon spectra are shown to exhibit ac Stark splitting of the states involved. The spectrum is a doublet for transitions to a stable final state and a triplet for transitions connected back to the initial, strongly driven state. The decay of an autoionizing state in the absence of a laser driving field is considered, and the square of the Fano qqq value is interpreted as the ratio of two decay rates.
Spectral features of the radiation emitted by autoionizing states in the presence of a strong laser field are calculated under the condition of multiple photon absorption and emissions. The method is based on the exact solution of the master equation for the recycled system. The decay spectra are found to exhibit sharp maxima at the laser frequency and, for large values of the Fano qqq value, sidebands which are reminiscent of the triplet which one finds in the context of a two-level atom.
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.
Absorption properties of a system consisting of two autoionizing states coupled strongly either by internal interactions or by external fields are investigated. The autoionizing states may themselves correspond to those induced by laser fields as in resonant multiphoton ionization. The analysis is based on the density matrices and incoherent processes like spontaneous emission and radiative recombination are included. Optical susceptibilities exist in a number of special cases for autoionizing transitions. Exact results for such optical susceptibilities are obtained. Explicit numerical results for susceptibilities, corresponding traditionally to strong-field inverse Raman effect, are given with a view to recent work on dc-field-coupled autoionizing states and on laser-induced autoionization. The behavior of both absorptive and dispersive parts is discussed for a range of parameters.
We present a formal theory and detailed calculations for phase-dependent laser-atom interactions involving autoionizing states. First, through simple models, we demonstrate that the simultaneous one- and three-photon excitation of one or two neighboring autoionizing states can exhibit profound changes of the line shape, as the relative phase of the two fields is varied from 0 to \ensuremath{\pi}. Through a proper choice of the field intensities and the phase, we obtain analytical results showing that one can cancel the transition to the discrete or the continuum part of the wave function, thereby leading to a flat or a completely symmetric line shape, respectively. At higher intensities, additional effects come into play, providing additional coupling between the discrete and continuum parts, which also exhibits a phase dependence. Finally, our theory is applied to a much more complex situation in Xe, involving many channels, not amenable to simple analytical expressions, but exhibiting nevertheless equally profound effects, including a modification of the branching ratio of two different products. The theory, which is here developed for atomic autoionization, is in fact fairly general and should pertain to related problems in any system involving discrete states embedded in continua.