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Physical Review Letters

Two-Photon Near-Resonance Light Scattering from an Atomic Level

J. Liran, L. A. Levin, G. Erez, Joshua Jortner

Published Feb 21, 1977• 10 citations
Publisher

Abstract

We have studied the time-resolved spectra, the energy-resolved spectra, and the total intensity of light emission induced by near-resonance two-photon excitation to the $4^{2}D_{\frac{3}{2}}$ and $4^{2}D_{\frac{5}{2}}$ levels of Na over the detuning range $\ensuremath{-}7 {\mathrm{cm}}^{\ensuremath{-}1}<~\ensuremath{\Delta}<~7 {\mathrm{cm}}^{\ensuremath{-}1}$. The time-resolved spectra of Na perturbed by Ar exhibit a fast adiabatic component and a slow resonance-fluorescence component. The cross section for phase-shifting, ${T}_{2}$-type collisions in this atomic system is $\ensuremath{\sigma}=110\ifmmode\pm\else\textpm\fi{}20$ ${\mathrm{\AA{}}}^{2}$.

DOI
10.1103/physrevlett.38.390

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Time-dependent spectra of light emitted after two-photon excitation with nonresonant intermediate state are studied by the perturbation method. Two components are distinguished: a slow one Is{I}_{s}Is​ connected with the excited-state population, and a fast one If{I}_{f}If​ connected with the double-quantum optical coherence. For large detuning of the two-photon frequency from the excited-ground-state energy separation, the fluorescent light is found to be ${I}_{s}\ensuremath{-}|{I}_{f}|$, and the Raman-scattered light is If{I}_{f}If​. The influence of statistics of light, laser linewidth, spectral bandwidth of the detector, and transfer of coherence from the ground to the excited state are also taken into consideration.
An experimental investigation of the atomic-Na 3s 2^{2}2${\mathit{S}}_{1/2--}$5s 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​ two-color two-photon polarization spectrum has been made. Measurements of the linear polarization degree of the two-photon transition were made for one laser tuned within a \ifmmode\pm\else\textpm\fi{}100 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range of the atomic-Na 3p 2^{2}2Pj{\mathit{P}}_{\mathit{j}}Pj​ levels, with the second adjusted to satisfy the two-photon resonance condition. The relatively short-pulse (\ensuremath{\sim}0.5 ns) lasers used eliminate effects on the spectrum due to atomic-Na hyperfine interactions and radiation trapping, while greatly reducing depolarization due to collisions with Ar gas. In the absence of collisions, the measured polarization spectrum is in excellent agreement with calculations. Measurements of the Ar pressure dependence of the spectrum revealed strong depolarization in the vicinity of resonant excitation through the 3p 2^{2}2P3/2{\mathit{P}}_{3/2}P3/2​ level. A collisional depolarization cross section of 200(30) \AA{} for this process was deduced from the data.
The cross sections for the excitation energy transfer induced by collisions with He, Ar and Na ground-state atoms have been measured. The sodium atoms in the 4D state have been produced by two-photon excitation using cw laser radiation at 578.89 nm. Within a model which takes into account collisional population and depopulation of the 4F level as well as radiative relaxation (direct or cascade) of the 3D, 4P, 4D and 4F states ending in the 3P level, the rate for the collisional transfer turns out to be related to the ratio of the steady-state populations created in 3D and 4D states. They have been determined by measuring the fluorescence intensities of the and transitions. The measurements yield the following cross section values for those processes investigated: , and , at .
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Light emission under near-resonant excitation by a pulsed optical field is described using a semiclassical (Bloch) model for the near-resonant transition. Adiabatic excitation of this transition leads to Raman emission, whereas nonadiabaticity gives fluorescence. The model describes quantitatively observed relaxation effects. It further predicts that such experiments can determine the power spectrum of the correlation function characterizing collisions, offering an alternative to off-resonance spectroscopy.
In the presence of coherent saturated near-resonant two-photon excitation, the ordinary Raman scattering line is replaced by a dynamic Stark shifted or Stark split doublet, and Rabi nutations appear in the time-resolved ordinary Raman spectrum. The relative intensity of the peaks of the doublet depends on the shape and on the average frequency of the exciting pulse. Striking new features arise from the interfering contributions of the upper and lower states of the two-photon transition to the Raman scattering process. The theory is applied to Raman scattering in atomic Na in the presence of the 3 2 S 1 2/(F=1, M F =1) to 4 2 D 3 2,5/2/(F=3,M F =3) two-photon resonances.