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Physical Review A

Double-resonance spectroscopy with fluctuating multimode fields: A Monte Carlo approach

H. M. Lauranto, Rainer Salomaa

Published Aug 1, 1997• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.56.1524

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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.
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.
This paper analyses the extraction of spectroscopic information on an atom via use of field fluctuations in a diode laser, wherein the statistics of diode-laser radiation are modeled by a phase-diffusion process. Using Monte Carlo methods, we solve density-matrix equations for a three-level V system, driven by this fluctuating field, tuned approximately to the two allowed transitions. The model is very general and allows us to incorporate arbitrary field strengths and bandwidths. We suggest two different signal detection schemes, each of which provides insight into different aspects of the energy-level structure in an atomic sample. Specifically, if intensity fluctuations in the field radiated from the sample are spectrally analyzed, via a homodyne technique, one can isolate contributions that are linear and quadratic in the radiated field, and these reveal resonances at the allowed transition frequencies of the atom. If we employ direct detection instead of the homodyne method, then the crossover transition is also revealed in the signal. The strengths of these resonances are very sensitive to the bandwidth of the field fluctuations, as well as the details of the field statistics. We also discuss the role of Stark shifts at higher intensities.
A theory of ac Stark splitting at double resonance in a three-level system is presented, the upper and lower transitions being coupled to a near-resonant intense multimode field and a weak monochromatic field, respectively. Linear response to a weak field is considered. The analytical treatment calling into action a diagram technique and the quasistationary-states method is carried out beyond the limits of perturbation theory and the nonresonant approximation. The multimode structure of the radiation spectrum results in a quasi-periodicity of the field-correlation function. It leads to a strong modulation of the absorbtion line shape with a period $\frac{1}{2}\ensuremath{\Delta}{\ensuremath{\nu}}_{0}$ where $\ensuremath{\Delta}{\ensuremath{\nu}}_{0}$ is the intermode interval. The role of different weakening effects such as spontaneous decay of the levels, the finite pulse duration, and instrumental and natural fluctuations of a single mode is studied. The last effect is shown to be the most important, and a possible method of direct measurement of the natural-fluctuations' correlation function is proposed.
The influence of relaxation parameters, as well as temporal fluctuations in the laser field on the modulation rate and phaseshift of the fluorescence from a two-level atom excited by a weakly modulated source is studied in detail. It is shown that, for intense resonant laser fields, the resonance in the modulation rate occurs at the modulation frequency Omega =2 due to the dynamical Stark splitting and has a width equal to 1 / 2 (T 1 -1 +T 2 -1 ). When temporal fluctuations of the exciting laser field are taken into account, the phaseshift of the scattered light is found to be strongly dependent on the bandwidth of the exciting source, as well as the frequency of modulation; hence experimental results on the determination of the lifetime by the phaseshift method have to be interpreted carefully. Numerical results for the modulation rates and phaseshift at different field strengths and various values of T 1 -1 , T 2 -1 , Delta laser bandwidth and Doppler broadening are presented.