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Physical Review A

Effect of spontaneous emission and recombination on the four-wave—mixing profiles involving autoionizing resonances

G. S. Agarwal, P. Anantha Lakshmi

Published Dec 1, 1983• 7 citations
Publisher

Abstract

A general expression for the four-wave---mixing profiles in situations involving autoionizing resonances is derived by taking fully into account the spontaneous-emission characteristics of the autoionizing states. The signals are valid for arbitrary values of Fano asymmetry parameters, field strengths, and spontaneous-emission rates. The dramatic increase in the four-wave---mixing signal for field strengths corresponding to the confluence is demonstrated. The spontaneous emission is shown to affect the line shapes not only in weak fields but also in strong fields. The effects of spontaneous emission are found to be most important for field strengths corresponding to confluence which is similar to the problem of laser-induced autoionization.

DOI
10.1103/physreva.28.3430

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Physical Review A•Apr 1, 1983•28 citations
A general expression for the four-wave---mixing profiles in situations involving autoionizing resonances is derived by taking fully into account the spontaneous-emission characteristics of the autoionizing states. The signals are valid for arbitrary values of Fano asymmetry parameters, field strengths, and spontaneous-emission rates. The dramatic increase in the four-wave---mixing signal for field strengths corresponding to the confluence is demonstrated. The spontaneous emission is shown to affect the line shapes not only in weak fields but also in strong fields. The effects of spontaneous emission are found to be most important for field strengths corresponding to confluence which is similar to the problem of laser-induced autoionization.
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.
The degenerate four-wave-mixing process in the vicinity of an autoionizing state is studied theoretically in the context of perturbation theory. The autoionizing state is represented either by an isolated Fano profile or by the appropriate expression of the multichannel quantum-defect theory for the corresponding Rydberg series of autoionizing states. Analytic expressions for the third-order susceptibility are given together with realistic numerical estimates based on atomic parameters extracted from accurate spectroscopic data. It is demonstrated that the observation of the effect is feasible in extensively studied atomic systems (e.g., alkaline earths) with existing coherent light sources. Constraints on the atomic parameters that will facilitate the experimental observation of the effect are identified and shown to be frequently met in real atomic systems.
Photoemission spectra from autoionizing states in the presence of a strong laser field are calculated. Such spectra have very sharp features near "confluence" (at the Fano minimum) and are very similar, in structure, to photoelectron spectra. The total intensity, as a function of laser intensity or detuning, has a peak near confluence, which can be used, among other things, for the accurate determination of Fano asymmetry parameter qqq.
Photon absorption spectroscopy is a powerful tool for uncovering the structure of atoms, molecules, and solids. Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures related to the structural and dynamical properties. Recently, Ott et al. [Science 340, 716 (2013)] successfully transferred Fano profile into Lorentzian line shape using an intense infrared laser, after excitation of autoionizing states in helium by attosecond XUV pulse. This is a very important step forward in quantum phase control. However, here we show experimentally that an autoionizing state can have both Fano and Lorentzian behavior naturally, depending on the process involved. This study utilized the inverse process of photon absorption ionization, i.e., electron ion recombination with photon emission, making sure the resonant autoionizing state is not modified or decorated by the laser fields. Our result implies that excitation of the state through different paths---for example, one photon versus multiphoton excitation, or even one step versus multistep excitation---can lead to different Fano profiles for the same resonant state. We also report an experimental determination of the energy shifts in the recombination photon-intensity peaks due to the interference between the resonant and nonresonant processes.
The exact solution of the Fano model, including both radiative recombination to the initial state (recycling) and off-diagonal phase-jitter relaxation, is obtained by two different methods. We derive a simple substitution rule stating that, by replacing $\ifmmode\pm\else\textpm\fi{}i{\ensuremath{\omega}}_{L}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}i{\ensuremath{\omega}}_{L}+{\ensuremath{\gamma}}_{T}$, the phase-jitter effects are included. The time dependence of the solution has a convolution form. The results for the electron spectrum exhibit an increasing elastic-peak line narrowing the faster the spontaneous decay becomes. For very fast spontaneous decay, the elastic linewidth saturates to ${\ensuremath{\gamma}}_{T}$. The relevant thresholds are discussed and demonstrated.