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Journal of Modern Optics

Optical pumping of the Na D2 transition with elliptically polarized light

Benjamin T. H. Varcoe, Robert T. Sang, W. R. Macgillivary, M. C. Standage, Peter M. Farrell

Published Apr 1, 1999• 13 citations
Publisher

Abstract

The quantum electrodynamic description of circularly and linearly polarized, single mode radiation exciting atomic transitions in a hyperfine manifold is extended to the more general case of elliptic polarization. Calculations for the sodium D2 line are tested by observing the line polarization of the resonance flourescence scattered perpendicular to the plane containing laser and atomic beams as a function of the laser polarization. Very good agreement between the calculations and the measurements is achieved. It is demonstrated that predetermined populations and substate coherences can be engineered by optically pumping the transition with the appropriately polarized radiation.

DOI
10.1080/09500349908231304

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Physical Review A•Jan 1, 1971•25 citations
The quantum electrodynamic description of circularly and linearly polarized, single mode radiation exciting atomic transitions in a hyperfine manifold is extended to the more general case of elliptic polarization. Calculations for the sodium D2 line are tested by observing the line polarization of the resonance flourescence scattered perpendicular to the plane containing laser and atomic beams as a function of the laser polarization. Very good agreement between the calculations and the measurements is achieved. It is demonstrated that predetermined populations and substate coherences can be engineered by optically pumping the transition with the appropriately polarized radiation.
The sodium D2{\mathit{D}}_{2}D2​ transition is resonantly excited by \ensuremath{\pi}-polarized, narrow-band laser radiation. The line polarization of the resulting fluorescence detected normally to the plane containing the electric-field vector of the radiation and its propagation direction, as well as the atomic beam, is measured as a function of radiation intensity and tuning. The data are compared to calculations from a quantum-electrodynamic theory which includes all participating energy states in the hyperfine representation. The quantitative agreement is very good.
The resonant excitation of the sodium D2 transition by laser radiation was investigated experimentally in this thesis. Line polarization measurement of the resonance fluorescence was employed to investigate the excitation process. The sodium atoms, which were collimated in a very narrow beam, were excited by a monochromatic laser beam with the frequency tuned to resonance with the 32S 112(F=2) - 32P312 hyperfine transition. The direction of the laser beam was perpendicular to the atomic beam and the fluorescence photons were detected along a direction perpendicular to both the laser and atomic beams. The experimental measurements were performed to determine the effect due to the variation of the laser intensity and frequency on the line polarization. A theoretical expression of the line polarization as a function of density matrix elements of the upper excited hyperfine sub -states was derived. A full quantum electrodynamic theory was used to derive an atomic operator equation of motion which was needed to calculate atomic operator elements. These elements then yielded the corresponding density matrix elements. The experimental results and the theoretical modelling were in a good agreement. The first experimental results for the line polarization of the highly excited states, 42D512 and 42D312, are also presented. The use of two lasers enabled these highly excited states to be excited. The line polarization of the fluorescence for transitions from the 4D level down to lower states is derived in terms of the density matrix elements of the upper excited states. Two limiting cases for the theoretical predictions of the line polarization are considered.
An experimental demonstration of the state-dependent nature of the forces exerted on an atom by resonant radiation is reported. Sodium atoms, which are contained in a highly collimated beam, are initially prepared in a particular ground hyperfine substate by optical pumping. They are then deflected by resonant laser radiation of known polarization. Measurements of the magnitude of the deflection show a dependence on the way the atoms were initially prepared, confirming the predictions of a recently developed theoretical model. The experimental data show good agreement with calculations of the theory using a full quantum electrodynamic description of the sodium transition involved.
A quantum-electrodynamic (QED) description of the resonant interaction of monochromatic light with the 32{3}^{2}32S1/2{\mathit{S}}_{1/2}S1/2​(F'=2)\ensuremath{\rightarrow}32{3}^{2}32P3/2{\mathit{P}}_{3/2}P3/2​(F=3,2,1) hyperfine transitions of the sodium D2{D}_{2}D2​ line is formulated in terms of the Heisenberg atomic operator. Off-diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences, and certain state coherences form a closed subset of the total system of equations. This subset is small enough to be computed numerically. The results of calculations with this model are compared with three previously developed semiclassical descriptions using the density operator. One of the semiclassical models was developed to describe the interaction of weak light with the atomic transition while another is suitable in the case of high-intensity light. For both \ensuremath{\pi} and \ensuremath{\sigma} excitation it is shown that the QED calculated values for the time-averaged, excited-level population probability converge to those of each of the semiclassical models in the appropriate limit of light intensity. For homogeneous broadening, results show that the optimum light intensity to obtain the largest fraction of atoms in the 32{3}^{2}32P3/2{P}_{3/2}P3/2​ level after transversing a 1-mm-diam laser beam is 1.15 mW/mm2{\mathrm{mm}}^{2}mm2 for \ensuremath{\pi} excitation and 1.43 mW/mm2{\mathrm{mm}}^{2}mm2 for \ensuremath{\sigma} excitation.
Doppler-free laser spectroscopy using polarization modulation has been carried out in Na D₁ and D₂ lines. The polarization of the pump beam is modulated between identically and orthogonally to a linear or circular polarization of the probe beam. The recorded signals of the hyperfine and crossover resonances are in agreement with a recent theoretical analysis of Nakayama which is based on velocity-selective optical pumping in a four-level system. Some exceptional discrepancy occuring in the D₂ is considered to be due to several relatively close lying resonances.
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.