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Journal of Modern Optics

The interference effect in the D 1 transition of the sodium atom generated by the hyperfine structure

Abu Mohamed Alhasan, Jan Fiutak

Published Jan 1, 2002• 4 citations
Publisher

Abstract

The steady state of the sodium atom interacting with linearly polarized light, tuned to the D1 transition, is analysed in terms of the density matrix components. The influence of the optical pumping and the collisional relaxation on the interference effect is investigated for the D1 transition dipole moment and the Raman coherences.
DOI
10.1080/09500340110095111

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Calculations of the collisional relaxation of electronic--nuclear polarization moments of all state of the fine and hyperfine structure of the 3/ital p//sup 2//ital P/ doublet of the sodium atom (/ital J/=1/2 and 3/2, nuclear spin /ital I/=3/2) are carried out. The case of selective monochromatic excitation of the fine level /sup 2//ital P//sub 1/2/, allowing for the overlap of the Doppler shapes of the hyperfine components of the spectral line, is discussed. Such excitation gives rise in the /sup 2//ital P//sub 1/2/ state to four groups of excited atoms differing in values of the velocity projection on the direction of the light beam. The problem of collisional relaxation of the polarization moments is solved for each of these groups of atoms, account being taken of the anisotropy of the velocity distribution and intramultiplet mixing. The alignment induced in the levels of the hyperfine structure of the /sup 2//ital P//sub 3/2/ state, populated by anisotropic collisions with atoms of different inert gases, is calculated, as is the linear polarization of the light of sensitized fluorescence. The calculation results are in good agreement with the experiment.

•Oct 1, 1988•0 citations
In the context of laser spectroscopy we consider the effects of interference between the spontaneous emission to a common lower level from neighbouring, closely spaced, excited-state levels. In particular the effects on the fluorescence spectrum and on the measured positions of the line centres are described. A formalism, based upon the atomic density matrix, is developed quantitatively to describe these effects within complex hyperfine systems such as the sodium D-lines. Where possible, we have tried to simplify the resultant equations, defining the magnitude of the various fluorescent components and establish a general result for the phase of each component. Finally, the formalism is applied to the particular case of the sodium D1-line, where very different results are obtained depending on whether optical pumping into unobserved states is included, or omitted, from the calculation.
The conventional $J=1/2\ensuremath{\leftrightarrow}J=1/2$ model is successful for the qualitative description of the interaction of sodium atoms and laser light tuned close to the atomic D1{D}_{1}D1​ transition. However, time constants for dynamic effects due to optical pumping predicted by the model are about an order of magnitude too short compared to experimental observations. The inclusion of hyperfine states in the quantum-mechanical description of the atom leads to a satisfactory model that also predicts the correct absorption due to atomic diffusion and allows for the description of effects related to population trapping. This hyperfine model is derived in detail and compared with the $J=1/2\ensuremath{\leftrightarrow}J=1/2$ approximation.
For pt. I see ibid. p. 231, 1994. We consider optical pumping in the multilevel sodium D 1 manifold by several coherent light fields. Coherence between atomic states is taken into account by solving the complete density matrix equations. The manifestation of population trapping and the variation of transmitted light intensity are predicted numerically and verified experimentally for the sodium D 1 line. The influence of relaxation and Doppler broadening is elucidated. The interaction of a strong and a weak field is shown to create electromagnetically induced transparency.
A new method has been designed for obtaining the hyperfine optical pumping of Na vapor. The pumping lamp is placed in a magnetic field and the light emitted in the field direction is used for excitation after crossing a circular polarizer selecting one of the Zeeman lines. This method has two interesting features: (i) The atoms can be pumped either in the lower or in the upper hyperfine sublevel by simply rotating a polarizer by an angle of $\frac{1}{2}\ensuremath{\pi}$; (ii) the hyperfine pumping is obtained using both the D1{D}_{1}D1​ and D2{D}_{2}D2​ resonance lines without filtering losses. The pumping efficiency is good and it has been possible to measure the spin-exchange cross section between sodium atoms by studying the hyperfine relaxation rates as a function of the sodium density. The result is ${\ensuremath{\sigma}}_{\mathrm{ex}}=(1.109\ifmmode\pm\else\textpm\fi{}0.005)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2.
Calculations of the collisional relaxation of electronic--nuclear polarization moments of all state of the fine and hyperfine structure of the 3/ital p//sup 2//ital P/ doublet of the sodium atom (/ital J/=1/2 and 3/2, nuclear spin /ital I/=3/2) are carried out. The case of selective monochromatic excitation of the fine level /sup 2//ital P//sub 1/2/, allowing for the overlap of the Doppler shapes of the hyperfine components of the spectral line, is discussed. Such excitation gives rise in the /sup 2//ital P//sub 1/2/ state to four groups of excited atoms differing in values of the velocity projection on the direction of the light beam. The problem of collisional relaxation of the polarization moments is solved for each of these groups of atoms, account being taken of the anisotropy of the velocity distribution and intramultiplet mixing. The alignment induced in the levels of the hyperfine structure of the /sup 2//ital P//sub 3/2/ state, populated by anisotropic collisions with atoms of different inert gases, is calculated, as is the linear polarization of the light of sensitized fluorescence. The calculation results are in good agreement with the experiment.