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Physical Review A

Temperature effects in the hyperfine spectrum of the D1 transition of sodium

Rajan S. Gurjar, K. K. Sharma

Published Jan 1, 1999• 2 citations
Publisher

Abstract

The velocity selective optical pumping technique has been used to obtain the Doppler-free spectrum of the $D1$ transition of sodium in the temperature range 110--169 \ifmmode^\circ\else\textdegree\fi{}C. The pump-induced changes in probe transmission across the Lamb dip and crossover resonances first increase and then decrease with temperature. We also observe a reversal in the relative magnitudes of these changes among some of the narrow resonances. These and other temperature-dependent features of the Doppler-free spectrum of the $D1$ transition of sodium are successfully explained within the framework of the composite five-level model. The degeneracies of the ground-state composite levels and the beam depletion effects at higher temperatures play a crucial role in these investigations.

DOI
10.1103/physreva.59.512

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Population changes among the hyperfine levels of the sodium D1 transition, created by a weakly saturating narrow-band pump, are detected by a counterpropagating probe in a 10-cm-long cell containing sodium vapor without any buffer gas. All Lamb dips and cross over resonances with linewidths approaching natural widths are clearly resolved. We have applied a five composite level model to interpret the observed probe absorption. The rate equations were solved analytically. The model predicts specific relationships between the frequency integrated probe absorption coefficient of crossover and Lamb dip resonances. We find excellent agreement in the case of crossover resonances that involve a single ground-state hyperfine level. The agreement is not so good for crossover resonances for which both ground hyperfine levels participate. \textcopyright{} 1996 The American Physical Society.

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Collision effects in velocity-selective optical pumping of sodium

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We report on a quantitative experimental investigation of velocity-changing collisions by means of velocity-selective optical pumping (VSOP). We have calculated the VSOP line shape for an atom with hyperfine structure with the use of two phenomenological kernels for the collision effects: the Keilson-Storer kernel, and a two-term kernel consisting of a broad Keilson-Storer part and a narrower Gaussian component. Corrections were included to account for the finite absorption in the sample and the backward reflection of the pumping beam. The experiments were carried out in sodium vapor with neon as the perturber gas. The ${D}_{1}$ line of sodium was used for optical pumping, and the orientation of the ground state was detected. Free parameters of the theory were determined by fitting the predicted line shapes to experimental curves. The Keilson-Storer kernel proved unsatisfactory, but the two-term kernel reproduced well the observed line shapes over the entire collision profiles in the neon pressure range 0-57 mtorr. In an independent experiment using rapidly modulated VSOP we also measured directly the cross section of velocity-changing collisions: $\ensuremath{\sigma}=(1.13\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$. The large weight obtained for the narrow Gaussian from the fits, as well as the collision cross section which is three times as large as the cross section deduced from tabulated gas kinetic radii, may indicate the presence of collisions with relatively small velocity changes in addition to hard-sphere encounters.

Physical Review A•Aug 1, 1983•36 citations
The velocity selective optical pumping technique has been used to obtain the Doppler-free spectrum of the D1D1D1 transition of sodium in the temperature range 110--169 \ifmmode^\circ\else\textdegree\fi{}C. The pump-induced changes in probe transmission across the Lamb dip and crossover resonances first increase and then decrease with temperature. We also observe a reversal in the relative magnitudes of these changes among some of the narrow resonances. These and other temperature-dependent features of the Doppler-free spectrum of the D1D1D1 transition of sodium are successfully explained within the framework of the composite five-level model. The degeneracies of the ground-state composite levels and the beam depletion effects at higher temperatures play a crucial role in these investigations.
Population changes among the hyperfine levels of the sodium D1 transition, created by a weakly saturating narrow-band pump, are detected by a counterpropagating probe in a 10-cm-long cell containing sodium vapor without any buffer gas. All Lamb dips and cross over resonances with linewidths approaching natural widths are clearly resolved. We have applied a five composite level model to interpret the observed probe absorption. The rate equations were solved analytically. The model predicts specific relationships between the frequency integrated probe absorption coefficient of crossover and Lamb dip resonances. We find excellent agreement in the case of crossover resonances that involve a single ground-state hyperfine level. The agreement is not so good for crossover resonances for which both ground hyperfine levels participate. \textcopyright{} 1996 The American Physical Society.
We present the results of a pump-probe laser spectroscopic investigation of the Doppler-broadened sodium D1D1D1 resonance line. We find 13 resonances in the resulting spectra. These observations are well described by the numerical predictions of a four-level atomic model of the hyperfine structure of the sodium D1D1D1 line. We also find that many, but not all, of these features can be understood in terms of processes originating in a two-level or three-level subset of the full four-level model. The processes we observed include forward near-degenerate four-wave mixing and saturation in a two-level system, difference-frequency crossing and nondegenerate four-wave mixing in a three-level V system, electromagnetically induced transparency and optical pumping in a three-level lambda system, cross-transition resonance in a four-level double-lambda system, and conventional optical pumping. Most of these processes lead to sub-Doppler or even subnatural linewidths. The dependence of these resonances on the pump intensity and pump detuning from atomic resonance are also studied.
Abstract We theoretically and experimentally investigate the Doppler-broadened absorption spectrum of the D2-line (52 S 1/2 → 52 P 3/2) in thermal (room-temperature) Rb vapour over a wide range of probe intensity, probe diameter, and vapour cell temperature to understand the effect of hyperfine pumping and transit-relaxation on the absorption lineshape. We present a relatively simple but comprehensive five-level rate equation model which incorporates optical pumping of the atomic population into the other ‘dark’ ground hyperfine level (leading to absorption saturation), including contributions of the three closely spaced (within one Doppler linewidth) hyperfine levels in the excited state 52 P 3/2 (allowed by the dipole transition selection rules). D2-line transmission spectra predicted by our model show excellent agreement (rms error < 5 % ) with the experimental data for a wide range of probe intensities (from ∼ 0.001 I s a t 0 all the way up to ∼ 10 I s a t 0 , where I sat0 is the usual two-level saturation intensity for the respective atomic transition), vapour cell temperatures (24.2°C–53.5 °C) and beam diameters (1/e 2 width ∼ 1 − 6 mm). Our model also takes into account the finite transit time of atoms across the probe beam cross-section, and correctly predicts the dependence of effective saturation intensity on probe diameter (up to ∼ 10 × lower saturation intensity as compared to I sat0 for few-mm beam sizes). This ab initio five-level model can thus predict accurate Doppler lineshapes for any given experimental parameter set for a linearly polarized probe without any fitting parameters, and can be easily applied to any other atomic system by an appropriate change of the atomic constants in the rate equations.
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.
We propose and demonstrate pump-probe spectroscopy of rubidium absorption that reveals the sub-Doppler hyperfine structure of the ${}^{5}{\mathrm{S}}_{1/2}\ensuremath{\leftrightarrow}{}^{5}{\mathrm{P}}_{3/2}$ (D2{\mathrm{D}}_{2}D2​) transitions. The counterpropagating pump and probe lasers are independently tunable in frequency, with the probe operating at the single-photon level. The two-dimensional spectrum measured as the laser frequencies are scanned shows fluorescence, Doppler-broadened absorption dips, and sub-Doppler features. The detuning between the pump and probe lasers allows compensation of the Doppler shift for all atomic velocities in the room-temperature vapor, meaning we observe sub-Doppler features for all atoms in the beam. We detail a theoretical model of the system that incorporates fluorescence, saturation effects, and optical pumping and compare this with the measured spectrum, finding a mean absolute percentage error of 3.11%. This high level of agreement allows us to extract the number density and temperature of the Rb\mathrm{Rb}Rb vapor from the two-dimensional spectrum. In the future this technique could be used as an atomic frequency standard for calibrating and characterising a single-photon or low-light-level source.
We report on a quantitative experimental investigation of velocity-changing collisions by means of velocity-selective optical pumping (VSOP). We have calculated the VSOP line shape for an atom with hyperfine structure with the use of two phenomenological kernels for the collision effects: the Keilson-Storer kernel, and a two-term kernel consisting of a broad Keilson-Storer part and a narrower Gaussian component. Corrections were included to account for the finite absorption in the sample and the backward reflection of the pumping beam. The experiments were carried out in sodium vapor with neon as the perturber gas. The D1{D}_{1}D1​ line of sodium was used for optical pumping, and the orientation of the ground state was detected. Free parameters of the theory were determined by fitting the predicted line shapes to experimental curves. The Keilson-Storer kernel proved unsatisfactory, but the two-term kernel reproduced well the observed line shapes over the entire collision profiles in the neon pressure range 0-57 mtorr. In an independent experiment using rapidly modulated VSOP we also measured directly the cross section of velocity-changing collisions: $\ensuremath{\sigma}=(1.13\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2. The large weight obtained for the narrow Gaussian from the fits, as well as the collision cross section which is three times as large as the cross section deduced from tabulated gas kinetic radii, may indicate the presence of collisions with relatively small velocity changes in addition to hard-sphere encounters.