3 + 2 photoionization of Xe in a pulsed, stochastic field

James C. Camparo, P. Lambropoulos

Published May 8, 1994• 0 citations

Abstract

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.

Related papers

ac Stark shift of a two-photon transition induced by a model stochastic field

James C. Camparo, P. Lambropoulos

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.

Journal of the Optical Society of America BDec 1, 199214 citations

Monte Carlo simulation of field fluctuations in strongly driven resonant transitions

James C. Camparo, P. Lambropoulos

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.

Physical Review AJan 1, 199323 citations

Multiphoton transitions in a colored vacuum: coupling of the ac Stark shift with spontaneous decay and the Lamb shift

James C. Camparo, P. Lambropoulos

In free space, where the vacuum mode density varies relatively slowly in the spectral region of an atomic transition, an atom’s real-field and vacuum interactions are effectively decoupled. Consequently, spontaneous decay and the Lamb shift are, for all practical purposes, independent of any real-field atomic perturbation. However, in a colored vacuum (i.e., a low-Q cavity) the vacuum mode density can change significantly in the vicinity of an atomic transition, so that a Stark shift will alter an atom’s vacuum environment and thereby couple real-field and vacuum effects. Since the ac Stark shift is an inherent aspect of multiphoton processes, this coupling is unavoidable for highly nonlinear field–atom interactions that occur in cavities. Here we consider this effect for 3+2 resonance-enhanced multiphoton ionization of xenon.

Journal of the Optical Society of America BMay 1, 20022 citations

Stochastic field effects and transform-limited laser pulses

James C. Camparo, P. Lambropoulos

In many ultrashort-laser-pulse experiments the field is transform limited, and under these conditions it is usually assumed that the stochastic nature of the field can be ignored in the interpretation of experimental data. We theoretically consider the 3 + 2 photoionization of xenon, using a pulsed stochastic field. Our results show that the field's stochastic nature always has an effect on the ac Stark shift modification factor Re(M), no matter what the pulse width, and that a short-pulse approximation to Re(M) can require a Fourier-transform bandwidth 1000 times larger than the laser's intrinsic (cw) spectral width.

Optics LettersOct 1, 19942 citations

Extreme Multiphoton Coupling in Molecular Systems

George N. Gibson

Compared to single-photon rates, multiphoton excitation rates of atoms and molecules are generally quite small, even at high laser intensities, at least in a 2-level system. Small multiphoton coupling strengths, large ac Stark shifts, and ionization all inhibit real population transfer between bound states. However, it has recently been shown that a 3-level system consisting of a ground state and a pair of nearly degenerate strongly coupled upper states greatly enhances the multiphoton coupling with the ground state, while also greatly reducing the ac Stark shift of the ground state. In this paper I will derive an analytic expression for the n-photon Rabi frequency, for this system, in the case of degenerate upper states, as well as an expression for the level shifts induced in the case of nondegenerate upper states. Numerical calculations based on the 3-level system are presented to verify the analytic results and to show that high-order {pi} pulses can be driven at moderate field strengths. To demonstrate the feasibility of this process in a real physical system, I will present fully correlated 2-electron calculations in a model one-dimensional molecular potential, including ionization that show a 12-photon {pi} pulse driven with near-infrared photons. In other words, amore » single excited state 18.6 eV above the ground state can be populated with over 90% efficiency with little ionization while the ground state is almost completely depopulated. Besides the possibility of producing an amplifying medium in the vacuum ultraviolet, this 3-level configuration may open the door to other strong field effects previously restricted to single-photon interactions, such as adiabatic passage and inner-shell ionization.« less

APSMay 1, 20030 citations

Non-Markovian stochastic jump processes. II. The case of resonance fluorescence

Abraham G. Kofman, Reuven Zaibel, Alfred M. Levine +1 more

Strong laser fields, when tuned on resonance to an atomic (molecular) transition, give rise to the well-known triplet of resonance fluorescence. The laser field is normally assumed to be strong and monochromatic, even though the spectrum of real lasers is never a \ensuremath{\delta} function. A standard way to treat laser fluctuations has been to assume a well-defined nominal frequency and a randomly fluctuating phase. Recently we introduced the generalized jump model (GJM) for correlated phase fluctuations, where correlated phase jumps are considered, leading to Markovian as well as non-Markovian stochastic behavior. In the GJM, each phase jump may be correlated to the previous jump, and the degree of correlation, the typical jump size, and the mean time between jumps are the three parameters defining the stochastic character of the laser field. In this paper we apply the GJM model to the case of resonance fluorescence from an atom excited by a stochastic field. The ``standard'' Mollow triplet is obtained in the monochromatic limit of small jumps, and several new predictions are made in the different limits of the stochastic parameters. In the small-jump limit, a new ``field effect'' is predicted. The spectral line shape and the triplet separation deviate from the Mollow predictions for a monochromatic field in a substantial way, giving rise to observable differences.In the highly correlated small-jump limit, which is approximated by the Kubo oscillator model, the previous results are corrected to include nonzero line shifts and extended to the case of non-Lorentzian line shapes. In all regions, even input fields of the same line shape (which would be considered identical in the one-parameter linewidth description) give rise to very different output spectra, justifying the more complete stochastic description. Effective relaxation constants ${\mathrm{\ensuremath{\Gamma}}}_{1}^{\mathrm{*}}$ and ${\mathrm{\ensuremath{\Gamma}}}_{2}^{\mathrm{*}}$ that simplify the description of the spectrum are calculated in all appropriate cases, and ${\mathrm{\ensuremath{\Gamma}}}_{1}^{\mathrm{*}}$ is found to equal the input laser linewidth. In addition to predicting the resonance fluorescence spectra, the present analysis provides a way to extract the stochastic parameters from the nonlinear measurement in those cases where the linear characterization of the input field cannot do it. The analytic work is fully supported by extensive numerical simulations.

Physical Review AJun 1, 199017 citations