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Journal of Physics B Atomic and Molecular Physics

Autoionisation in a non-Markovian collisional dephasing process

Zhifang Deng

Published Jun 28, 1985• 6 citations
Publisher

Abstract

The authors study an autoionisation model undergoing a collisional dephasing process. The photoelectron spectrum is defined in terms of the tetradic scattering formulation. The theory uses projection operator techniques in Liouville space to perform selective averagings over the bath variables. In the weak-field case, the long-time photoelectron spectrum is derived and calculated, and it is expressed by the single-photon lineshape functions. The authors' result enables one to analyse the Markovian and non-Markovian lineshapes. They show the different aspects of the spectrum in these two cases.

DOI
10.1088/0022-3700/18/12/017

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The authors study an autoionisation model undergoing a collisional dephasing process. The photoelectron spectrum is defined in terms of the tetradic scattering formulation. The theory uses projection operator techniques in Liouville space to perform selective averagings over the bath variables. In the weak-field case, the long-time photoelectron spectrum is derived and calculated, and it is expressed by the single-photon lineshape functions. The authors' result enables one to analyse the Markovian and non-Markovian lineshapes. They show the different aspects of the spectrum in these two cases.
We present a general microscopic theory for near resonance light scattering (RLS) from collisionally perturbed atoms and molecules. The theory is based on the tetradic scattering formalism of Fano and Ben-Reuven. We perform a systematic density expansion and show that the four-time, many-body, dipole correlation functions necessary for the evaluation of the RLS cross section may be rigorously expressed (to lowest order in pressure) in terms of three single-particle, two-time, correlation functions, two of which are associated with the absorption and emission line broadening and the third is a cross correlation function. Our most general expressions are valid for an arbitrary value of the bath correlation time (relative to the broadening), and interpolate smoothly all the way from the static limit of inhomogenous broadening up to the reverse, the Markovian (homogenous) limit. The stochastic Gaussian model of Takagahara, Hanamura, and Kubo is obtained also as a special case of the present formulation.
In the theoretical study of photoionization, certain properties of the photoelectrons are not defined in terms of any (even idealized) model for the electron-detection process, in contrast to the well-known Glauber theory of photon detection. Thus, for instance, the energy spectrum of the electron produced in atomic ionization is usually defined simply as the long-time probability for the electron to have a given energy. In this paper a formal model for an electron detector localized to a small region in space, similar to the DeWitt monopole detector, is set up in terms of which results analogous to those obtained for photon detection in the Glauber theory can be obtained. In addition, it is possible to define correlation functions describing the joint probability of detecting an electron and a photon. This correlation function is calculated here in the case of two-photon ionization of an atom modeled as having two discrete energy levels and an ionization continuum. When the atom is subjected to an incident driving field, both a photoelectron and scattered photons arising from the spontaneous decay of the upper of the two discrete levels are produced. Correlations between these photons and the photoelectron are studied here by considering the joint probability of detection of a photoelectron and a scattered photon for a monochromatic driving field.
Atoms in an autoionisation state can be excited to higher states in the continuum as well as performing spontaneous transitions to bound states by laser-induced autoionisation. Both effects are investigated by means of the reaction matrix. Results obtained by Armstrong et al (1978) using the same method are extended. The shape of the photoelectron spectrum is different from that of the photon spectrum emitted from the autoionisation state but is similar to that of the photon spectrum emitted from the same bound state which is excited to the ionisation states in the former case. It is predicted that the shape of the fluorescence yield with the pump laser detuning is Lorentzian. The multiphoton process contributes to the photoelectron spectrum in a complicated way.
The authors study the resonance lineshape in two-photon ionisation of atoms when the power broadening due to the bound-bound transitions is by far the dominant broadening mechanism. The authors consider the effect on the lineshape of turn-on of the laser-atom interaction, spontaneous emission and laser linewidth, and show that several different types of lineshapes can result depending on the conditions involved. The authors also consider the photoelectron spectrum, and show that it is also sensitive to these same parameters.
A non-markovian model of the detection of cavity photons is proposed. The cavity photons interact with the atoms of the detector in a two-stage process, while the evolution of the cavity photons is modelled, as usual, as a population process with constant rate parameters. The joint distribution of the cavity photons and the number of detected photoelectrons is studied. The results corresponding to the markovian model proposed by Shepherd are recovered by an appropriate limiting procedure. Some simple characteristics of the twofold counting statistics are also obtained. In particular, the memory effects of two-stage detection are shown to result in a depletion of bunching; the shape of the spectrum (in the time domain), while similar to that obtained using the Shepherd model, is depressed pointwise by a memory-dependent factor.
An expansion is presented for the absorption lineshape of a two-level system in a strong radiation field being perturbed by dephasing collisions, within the binary collision approximation. No dynamical assumptions regarding the time scale of the collisions (relative to the broadening) need to be made and the present theory interpolates smoothly between the impact and the quasistatic limits. The present solution reduces in weak radiation fields to the linear unified theory of spectral lineshapes and in the impact limit (fast collisions) the authors recover the Karplus-Schwinger formula. The only molecular information necessary for the exact evaluation of the absorption lineshape in a strong field is the same single-particle correlation function g( tau ) which appears in the linear (weak field) unified theory.