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Physical Review A

Laser-induced autoionization in the presence of radiative damping and transverse relaxation

Joseph W. Haus, Maciej Lewenstein, Kazimierz Rza̧żewski

Published Oct 1, 1983• 31 citations
Publisher

Abstract

A model for laser-induced autoionization is considered which includes two qualitatively different relaxation mechanisms: radiation damping to the ground state and phase fluctuations. Analytic solutions are presented for the first- and second-moment correlation functions of the atomic and photon operators in the Heisenberg picture. We present an explicit analysis of the spectrum of emitted photons at long times and investigate the effect of both relaxation mechanisms, as well as the influence of detuning and laser intensity, on this photoemission spectrum.

DOI
10.1103/physreva.28.2269

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A model for laser-induced autoionization is considered which includes two qualitatively different relaxation mechanisms: radiation damping to the ground state and phase fluctuations. Analytic solutions are presented for the first- and second-moment correlation functions of the atomic and photon operators in the Heisenberg picture. We present an explicit analysis of the spectrum of emitted photons at long times and investigate the effect of both relaxation mechanisms, as well as the influence of detuning and laser intensity, on this photoemission spectrum.
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.
Using an exactly soluble model for the radiative coupling of bound and autoionizing states, we explore the modification in the shape of the photoemission spectra and the total number of scattered photons (photon yield) resulting from finite interaction times. The photon yield studied as a function of the laser-field amplitude (Rabi frequency) or laser–atom detuning has a maximum. This maximum narrows and in certain circumstances shifts as the interaction time is. increased. Near the confluence of coherences the finite time spectra exhibit a rich structure; the heights and widths of the peaks, as well as their positions, are sensitively dependent on the interaction time. Moreover, the narrow central peak is accompanied by strong periodic wiggles, whose period is inversely proportional to the interaction time. The effects of laser broadening on the spectra are fully accounted for. Furthermore, the algebraic expressions for the ground-state occupation probability and the photon yield are considerably simplified from those of our previous analysis of the problem.
Detailed descriptions of one- and two-photon ionization are presented. We go beyond conventional perturbation theory to investigate the dynamics of both processes for a broad range of field intensities. The general theory of unstable decaying states is applied to the problem of one-photon ionization (the photoeffect). It is found that a non-trivial dependence of the transition dipole moment on the continuum state energy can lead to corrections to exponential decay, and even oscillations in the bound state population. As examples we consider the photoionization of hydrogen and atoms with autoionizing states. Only in the absence of autoionizing states corrections to exponential decay remain inconsequential for any experimentally relevant intensity. Our description of two-photon ionization is formulated in the Heisenberg picture. Besides the usual two-level atom projection operators we introduce explicitly the operators referring to the atomic continuum. By eliminating from the equations of motion the terms related to the electromagnetic self field as well as the terms referring to the continuum, transverse and longitudinal damping corresponding to spontaneous emission and photoionization is obtained. The use of field correlation functions allows us to account for the partial coherence of the applied field. We develop a technique to extract from the equations of motion a unique two-photon ionization rate. Such a characterization of the ionization process is not only instructive because of its simplicity, it is also in many cases completely satisfactory. The resulting general expression for the two-photon ionization rate is the central result of our treatment. From it we recover several familiar results in different limiting cases. In addition, our general rate expression provides the first description of the complete hierarchy of saturation effects that one should expect. We present a number of examples where we calculate the two-photon ionization rate as a function of the detuning, and where we emphasize the saturation and field correlation effects.
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.
Atoms in doubly excited states above the first ionization limit can decay via autoionization in which an electron is emitted leaving an ion, or by photoemission which leaves the atom in a singly excited state. In this paper, it is demonstrated that interaction between the atoms and a laser pulse that is short compared to the autoionization lifetime can lead to large enhancement of the photoemission process by stimulating the atoms to emit a photon. Since the resultant singly excited atoms do not autoionize, this process can be viewed as an enhancement of the stabilization of the doubly excited atoms against autoionization. A simple theoretical model is outlined that shows good agreement with the experimental results.
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.