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Journal of the Optical Society of America B

Finite interaction times and laser-bandwidth effects on the photoemission from an autoionizing atom

Joseph W. Haus, Maciej Lewenstein, Kazimierz Rza̧żewski

Published Aug 1, 1984• 7 citations

Abstract

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.

DOI: 10.1364/josab.1.000641

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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.

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

q

value is interpreted as the ratio of two decay rates.

Strong laser-field-induced autoionisation in the presence of both photoionising and radiative decay of the autoionising state (AS) is investigated, focusing on the laser intensity dependence of the photoemission and photoelectron spectra. In contrast to previous predictions, power broadening and increasing reduction of the doublet peak heights with field strength are found in the photoemission spectrum. Similar effects leading to considerable suppression and even complete disappearance of the lowest-order peaks in the photoelectron spectrum, together with peak switching, are also demonstrated, which are closely related to above-threshold ionisation. In addition, it is suggested that the total number of energetic photoelectrons may serve as an alternative to measuring the atomic parameters of the AS. All these effects are attributed to the presence of the strong 'probe': laser-induced decay of the AS.

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.

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

q

.

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 authors investigate two-photon ionisation using a generalised rate equation technique for a model in which the atom is assumed to have only two bound levels (the ground state and an excited state) together with a simple continuum of ionised states. Spontaneous emission is allowed from the excited to the ground state, and the laser is assumed to have a finite bandwidth due to phase diffusion. The photoelectron energy distribution is calculated; it is found that if the Rabi frequency exceeds the ionisation rate the energy spectrum is a sensitive function of the linewidth and spontaneous emission rate, whereas if the ionisation rate exceeds the Rabi frequency then the sensitivity of the energy spectrum to these parameters depends upon the initial state of the system. A quite small value of laser linewidth is found to considerably reduce the heights of peaks and increase the widths. Analytic and numerical results are presented.