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Physical Review A

Composite level approach to the hyperfine structure of the sodiumD1 transition

Rajan S. Gurjar, K. K. Sharma

Published Feb 1, 1996• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.53.969

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

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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.

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Abstract An experiment on the saturated absorption spectroscopy (SAS) of 87Rb-D2 line is performed using the Laguerre–Gaussian (LG) beam as structured light. The theoretical simulation of which is done by considering a four-level atom-laser coupled system. The theoretically simulated spectra fairly match with the experimentally observed spectra. The line-width narrowing behavior of both the observed hyperfine and crossover resonances in the Doppler-broadened probe absorption spectra is attributed by the spatially dependent Rabi frequency of the pump LG beam irrespective of the characteristics of the probe beam. The results also illustrated that the narrowing behavior of the line shapes of the hyperfine structure using the LG beam is universal in nature, i.e. irrespective of hyperfine or crossover transitions. This structured light-induced narrowing of line-width of the sub-Doppler hyperfine and crossover resonances can be utilized for high-precision laser frequency locking at a particular hyperfine or crossover transition. Moreover, a significant narrowing of hyperfine and crossover resonances with the variation of the orbital angular momentum (OAM) number of the LG beam shows that the generated SAS signal can be manipulated by using the OAM of the structured light as a control knob.

Physica Scripta•Nov 13, 2024•1 citation
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.
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.
Saturated absorption spectroscopy linewidths down to half the natural linewidth have been obtained for the sodium D1{\mathit{D}}_{1}D1​ transition in a strongly absorbing gas cell. The strong-line-narrowing effect is achieved by using an experimental ``tandem'' approach with two absorbing cells in series, where the saturated absorption output from the first cell is used as an input beam for a saturated absorption measurement in the second cell. A physical interpretation of the line-narrowing mechanism in highly absorbing media is presented, which, among other things, explains why the narrowing effects are different for crossover transitions. It is further argued that in these experiments the line-narrowing effect is caused by optical pumping and can be appropriately described by rate equations. This is different from several other recent papers on high-contrast transmission spectroscopy, where full Bloch vector models were necessary to fully describe the line shapes. Here a rate equation model, which includes two spatial dimensions, is developed, and reasonable agreement is obtained between experimental and theoretical data. \textcopyright{} 1996 The American Physical Society.
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.
Optical pumping of the ground states of sodium can radically alter the shape of the laser-induced fluorescence excitation spectrum, complicating measurements of temperature, pressure, etc., which are based on these spectra. Modeling of the fluorescence using rate equations for the eight hyperfine states of the sodium D manifolds can be used to quantify the contribution to the ground state pumping of transitions among the hyperfine excited states induced by collisions with buffer gas atoms. This model is used here to determine, from the shape of experimental spectra, cross sections for $\ensuremath{\Delta}F$ transitions of the P3/2{P}_{3/2}P3/2​ state induced by collisions with helium and argon atoms, for a range of values assumed for the ${P}_{1/2}, \ensuremath{\Delta}F$ cross sections. The hyperfine cross sections measured using this method, which to our knowledge is novel, are compared with cross sections for transitions involving polarized magnetic substates mF{m}_{F}mF​ measured previously using polarization sensitive absorption. Also, fine-structure transition $(\ensuremath{\Delta}J)$ cross sections were measured in the pumped vapor, giving agreement with previous measurements made in the absence of pumping.
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 An experiment on the saturated absorption spectroscopy (SAS) of 87Rb-D2 line is performed using the Laguerre–Gaussian (LG) beam as structured light. The theoretical simulation of which is done by considering a four-level atom-laser coupled system. The theoretically simulated spectra fairly match with the experimentally observed spectra. The line-width narrowing behavior of both the observed hyperfine and crossover resonances in the Doppler-broadened probe absorption spectra is attributed by the spatially dependent Rabi frequency of the pump LG beam irrespective of the characteristics of the probe beam. The results also illustrated that the narrowing behavior of the line shapes of the hyperfine structure using the LG beam is universal in nature, i.e. irrespective of hyperfine or crossover transitions. This structured light-induced narrowing of line-width of the sub-Doppler hyperfine and crossover resonances can be utilized for high-precision laser frequency locking at a particular hyperfine or crossover transition. Moreover, a significant narrowing of hyperfine and crossover resonances with the variation of the orbital angular momentum (OAM) number of the LG beam shows that the generated SAS signal can be manipulated by using the OAM of the structured light as a control knob.