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Physical Review A

Model description of the transit-time problem for fast particles crossing a laser beam

S. D. Chekhovskoi, Leonti N Labzowsky

Published Jun 21, 2024• 0 citations
Publisher

Abstract

The model description of the spectral line broadening for atoms crossing the laser beams is presented. The combined effect of the transit-time broadening, natural broadening, and transverse Doppler broadening is considered. This is done by introducing one-parametric adiabatic damping of atom-laser interaction where the particles interact with the laser during a finite time interval. The simplest rectangle distribution of the light intensity inside the laser beam is employed. The dependence of absorption probability on the transit time for different detunings is calculated and compared with earlier results. The limits for using the Lorentz line profile for describing the interaction of fast particles with laser beams are established.

DOI
10.1103/physreva.109.062811

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The model description of the spectral line broadening for atoms crossing the laser beams is presented. The combined effect of the transit-time broadening, natural broadening, and transverse Doppler broadening is considered. This is done by introducing one-parametric adiabatic damping of atom-laser interaction where the particles interact with the laser during a finite time interval. The simplest rectangle distribution of the light intensity inside the laser beam is employed. The dependence of absorption probability on the transit time for different detunings is calculated and compared with earlier results. The limits for using the Lorentz line profile for describing the interaction of fast particles with laser beams are established.
The paper is devoted to the investigation of the absorption of ultrashort laser pulses on atoms in plasmas, accounting for the different broadening mechanisms of atomic resonant transitions. The analysis is made in terms of the absorption probability during the entire interaction between the laser pulse and atom. Attention is mainly given to dependence of probability upon the pulse duration and the carrier frequency of the pulse. The results are presented via dimensionless parameters and functions describing the effect of finite pulse duration on atomic spectra for different broadening mechanisms, namely Doppler, Voigt, Holtsmark and their combinations, as well as the Stark line broadening of Rydberg atomic lines.
We revisit transit time broadening for one of the typical experiment designs in molecular spectroscopy, that of a collimated supersonic beam of particles crossing a focused Gaussian laser beam. In particular, we consider a Doppler-free arrangement of a collimated supersonic beam of Na2{}_{2}2​ molecules crossing two counterpropagating laser beams that excite a two-photon transition in a three-level ladder scheme. We propose an analytical two-level model with a virtual intermediate level to show that the excitation line shape is described by a Voigt profile and provide the validity range of this model with respect to significant experimental parameters. The model also shows that line broadening due to the curvature of laser field wave fronts on the particle beam path is exactly compensated by increased transit time of particles farther away from the beam axis, such that the broadening is determined solely by the size of the laser beam waist. The analytical model is validated by comparing it with numerical simulations of density-matrix equations of motion using a split propagation technique and with experimental results.
A weak excitation transit-time resolution limited analytic line shape is derived for a Doppler broadening-free degenerate two-photon transition from a standing wave with a TEM00 transverse profile. This approximation is appropriate when the collisional mean free path is much larger than the transverse width of the TEM00 beam. It is considerably simpler than the two-photon absorption line shape previously published, Bordé, C. R. Hebd. Seances Acad. Sci., Ser. B 282, 341–344 (1976), which was derived for more general experimental conditions. The case of a saturating field, with an intensity-dependent shift of the resonance frequency, is treated and expressed in reduced units. Numerical calculations are presented for the line shape for a range of the reduced intensity and light intensity shifts values.
We investigate the process of photon absorption by atoms or molecules shortly interacting with a laser beam in the dipole approximation. Assuming that the interaction time $\ensuremath{\tau}$ is much smaller than the lifetime of the corresponding excited state, we examine the absorption probability as a function of $\ensuremath{\tau}$. In addition, we incorporate Doppler broadening due to nonzero temperature of the atoms (molecules). It is demonstrated that in the case of a zero detuning and without Doppler broadening the absorption probability is quadratic in $\ensuremath{\tau}$. Once Doppler broadening is taken into account or the laser beam is off from the resonant frequency, the absorption probability becomes linear in $\ensuremath{\tau}$. Our findings are expected to be important for experimental studies in optical cells or cavities where atoms or molecules traverse continuous laser beams. The experimental prospects of searching for the electric dipole moment of the electron are discussed in detail.
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