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Physical Review A

Monte Carlo simulation of field fluctuations in strongly driven resonant transitions

James C. Camparo, P. Lambropoulos

Published Jan 1, 1993• 23 citations
Publisher

Abstract

We have developed a theoretical approach to the study of field-fluctuation effects on nonlinear resonant transitions based on a Monte Carlo simultation. In this paper, we present a description of the model, as well as results from its application to ac Stark splitting in double-optical-resonance driven by a two-photon transition.
DOI
10.1103/physreva.47.480

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We have developed a computational framework for the study of the effects of field fluctuations on strongly driven nonlinear transitions. Nonlinearity may stem from cither the strong coupling (saturation) of a resonant transition or its multiphoton character, or it may stem from both in the most general case. Our approach is based on a Monte Carlo simulation of stochastic field fluctuations, which allows maximum flexibility in the stochastic nature of the field and in the type of process that is studied. Here, we report on a more general problem than has previously been considered in the interaction of atoms with stochastic fields, namely, the three-photon resonant five- photon ionization of xenon, 3 + 2 photoionization of xenon has been the subject of a fair number of experimental investigations. It involves nonlinearity in with a bound-bound and a bound-free transition as well as an ac-Stark shift. Consequently, there are correlations among three fluctuating parameters: the three-photon Rabi frequency, the two-photon ionization rate, and the intensity-dependent ac-Stark shift, and it is these correlations that make the stochastic-field problem almost intractable to traditional methods of analysis.
A three-level cascade system coupled to two pulsed, fluctuating multimode laser fields is studied with numerical Monte Carlo simulations. Laser noise is modeled by introducing abrupt, random variations into the field parameters. We show that both phase and amplitude fluctuations may increase the signal through the ac Stark effect, and we demonstrate how noise can change the whole spectral structure of the transitions. As a result that is conveniently produced with simulations but that is often difficult to attain analytically, we also present on- and off-resonance signal distributions at various saturation levels and in different noise scenarios.
We have investigated the ac Stark shift of a two-photon transition induced by a model stochastic field by using a Monte Carlo technique. The model field has a stochastic single mode, which can possess both colored amplitude and colored frequency fluctuations. The stochastic field’s modification of the ac Stark shift is quantified by a parameter M, which is the ratio of the Stark shift in the model stochastic field to the Stark shift that would be obtained in a phase-diffusion field of equivalent linewidth (i.e., a field with frequency fluctuations but no amplitude fluctuations). In the regime of weak fields, below saturation of the bound-bound transition, we find that M is greater than unity: the Stark shift is enhanced by the stochastic field. Moreover, in this regime M is an increasing function of the field’s degree of photon bunching. In strong fields, where the bound–bound transition is nearly saturated, the enhancement of the Stark shift is diminished, so much so that in extremely strong fields M is actually less than unity. Our calculations indicate that the ac Stark shift’s modification occurs through two distinct processes, depending on the strength of the field. In weak fields enhancement of a multiphoton transition’s Stark shift is influenced primarily by the intrinsic correlation between ac-Stark-shift fluctuations and Rabi-frequency fluctuations. In strong fields the fluctuating Stark shifts give rise to an asymmetric resonance line shape in a fashion analogous to inhomogeneous broadening. The line shape’s peak position then has a sublinear dependence on the stochastic field’s intensity, and this yields a diminished value of M.
A detailed theoretical analysis of ac Stark splitting in double optical resonance and resonance fluorescence by a nonmonochromatic complex chaotic field is presented. It is shown that a one-photon transition undergoes Stark splitting, which is strongly affected by the intensity fluctuations of the chaotic light. On resonance, the lines in the doublet structure of double optical resonance and the sidebands of the triplet structure in resonance fluorescence are broadened by the intensity fluctuations and tend to copy the Rayleigh distribution of the field amplitude. Off resonance, the asymmetry of the doublet in double optical resonance is reversed and a sideband asymmetry appears in resonance fluorescence for finite bandwidth of the incident light. While on resonance the splitting is always reduced, off resonance the intensity fluctuations may lead to an enhancement of the splitting in comparison to phase-diffusing light.
The parametric resonances and the quasi-level structure of an atom strongly driven by a near-resonant amplitude-modulated optical field are studied theoretically. An approximate analytical solution of the density-matrix equations of motion is obtained for two-level and three-level atoms. Based on this solution the quasi-level shifts are analyzed, and the conditions for the quasi-levels to cross each other are derived. Expressions are given for the probe-wave absorption/gain spectrum near the parametric resonance and far from it. It is pointed out that the parametric resonances appear when the pumping field sidebands are tuned to resonance with some transitions among the quasi-levels.