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Physical Review A

Rate of resonant two-photon ionization in the presence of a partially coherent radiation field

Jacob L. F. de Meijere, Joseph H. Eberly

Published Apr 1, 1978• 87 citations
Publisher

Abstract

A treatment is given of two-photon ionization in which particular attention is paid to the influence of the bandwidth of the ionizing light on the ionization rate. The model adopted for the atom is a common one, including two bound levels and a continuum. The model of the laser is general enough to allow short-term temporal fluctuations of amplitude or phase, and these fluctuations give rise to the laser bandwidth. It is found that the fluctuations have the most interesting effects on the ionization rate when the laser coherence time is shorter than the atomic memory time, as could be expected. In addition to laser bandwidth, we consider the influence on the ionization rate of the detuning of the laser from the intermediate-state resonance, the laser power, and the finite lifetime of the intermediate state. Comparisons with related earlier calculations are made and similarities and differences are pointed out.

DOI
10.1103/physreva.17.1416

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A treatment is given of two-photon ionization in which particular attention is paid to the influence of the bandwidth of the ionizing light on the ionization rate. The model adopted for the atom is a common one, including two bound levels and a continuum. The model of the laser is general enough to allow short-term temporal fluctuations of amplitude or phase, and these fluctuations give rise to the laser bandwidth. It is found that the fluctuations have the most interesting effects on the ionization rate when the laser coherence time is shorter than the atomic memory time, as could be expected. In addition to laser bandwidth, we consider the influence on the ionization rate of the detuning of the laser from the intermediate-state resonance, the laser power, and the finite lifetime of the intermediate state. Comparisons with related earlier calculations are made and similarities and differences are pointed out.
We study three ways in which two-photon ionization, at high light intensities and near an intermediate-state resonance, may be described. We calculate the instantaneous ionization rate, the total ion count, and a saturable rate constant. We find that the total ion count, which is the experimentally interesting quantity in most cases, is very closely modelled by our saturable rate constant. The instantaneous ionization rate bears no useful relation to the total ion count in many cases. In comparing these three descriptions of ionization we have included the effects of detuning from resonance, finite light bandwidth, finite intermediate-state lifetime, and light intensity; we have varied all of these parameters independently over several orders of magnitude. Our conclusions are in good agreement with, and extend the findings of, Ackerhalt and Shore
A time-independent single-rate theory for multiphoton ionization processes is developed to cover cases with a partially coherent (finite-bandwidth) driving laser. We use the Ornstein-Uhlenbeck fluctuating-phase model to describe the driving field, which has therefore a non-Lorentzian spectrum, and the effective two-level model to represent the atomic system. We present analytic and numerical methods that permit discussion of the effects of non-Lorentzian band-shape laser light, and we give analytically the bandwidth dependence of the rate in the wings of the ionization curve. Our model contains a simple scaling relationship that permits the rate for NNN-photon-resonant (N+1N+1N+1)-photon ionization to be obtained directly from the one-photon-resonant two-photon ionization rate. We treat explicitly the cases N=1N=1N=1 and N=2N=2N=2.
Presents a theoretical analysis of the effect of laser light statistics on two-photon resonant three-photon ionisation of sodium. The ionisation probability and the population of the atom in the resonant state are compared in the presence of an intensity stabilised laser with a diffusing phase (phase diffusion model) and light undergoing Gaussian amplitude fluctuations (chaotic field). In the limit of large bandwidth fields the resonant two-photon excitation is statistically decoupled from the following ionisation step. A decrease of the bandwidth results in a partial correlation between these two steps manifesting itself in an enhancement of the ionisation probability in the chaotic field. With increasing intensity and the onset of saturation of the bound-bound transition, the ionisation probability and resonant excited-state population in the chaotic field may become smaller than the one in the phase diffusing light. In the large-bandwidth limit the Stark shift in the chaotic field is enhanced, which has a pronounced effect on the effective power-law dependence of the ionisation probability.
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 effect of temporal coherent control on the two-photon-resonant third-harmonic generation and multiphoton ionization into the continuum states of an atomic system is experimentally and theoretically investigated by means of a pair of partially incoherent, identical laser pulses. The evidence of quantum interference as a function of the delay between the pulses is reported. The transition from the resonant to the nonresonant case is also shown. The obtained results agree with the prediction of a theoretical model showing that the onset of quantum interference appears to be related to the coherence time of the laser radiation, which is much shorter than the pulse duration.