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Photonics North (PN)

Straightforward Measurement of Saturation Intensity of Doppler-Broadened Transitions: Application to Rubidium Vapour

Omid Mozafar, Varun Sharma, R. Margoth Córdova‐Castro, Akbar Safari, Jeremy Upham, Robert W. Boyd

Published May 28, 2024• 0 citations
Publisher

Abstract

The commonly quoted saturation intensity of rubidium (Rb) for D2 transitions is 16.7$\mathrm{W}.\mathrm{m}^{-2}$. This value, however, is only accurate for the cycling transition, which renders the Rb atom to resemble a two-level system. In practice, the effective saturation intensity is influenced by various factors, such as the polarization of light, optical pumping, and atom collision which can redistribute the population. As a result, it is crucial to experimentally determine the effective saturation intensity. In this context, we demonstrate a novel yet simple experimental method to measure the effective saturation intensities of Doppler-broadened transitions in atomic vapours. Our method only requires on-resonance absorbance data for various input laser intensities, which can be obtained with a tunable CW laser without the need for precise frequency locking. We applied this method to measure the effective saturation intensities of all four Doppler-broadened D2 transitions in natural rubidium (Rb) vapour (27.8%87Rb and 72.2 %${}^{\text{8}} {}^{\text{5}}Rb$) at$r={35}^{\circ} \mathrm{C}$. The results show that the effective saturation intensities for Rb range from 0.752 to 16.8$\mathrm{W}.\mathrm{m}^{-2}$. Notably, for certain transitions (specifically, repump transitions), the effective saturation intensities were smaller than 16.7 W.$\mathrm{m}^{-2}$(up to an order of magnitude), with potentially important implications for optical pumping in Doppler-broadened transitions.

DOI
10.1109/pn62551.2024.10621806

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The commonly quoted saturation intensity of rubidium (Rb) for D2 transitions is 16.7W.m−2\mathrm{W}.\mathrm{m}^{-2}W.m−2. This value, however, is only accurate for the cycling transition, which renders the Rb atom to resemble a two-level system. In practice, the effective saturation intensity is influenced by various factors, such as the polarization of light, optical pumping, and atom collision which can redistribute the population. As a result, it is crucial to experimentally determine the effective saturation intensity. In this context, we demonstrate a novel yet simple experimental method to measure the effective saturation intensities of Doppler-broadened transitions in atomic vapours. Our method only requires on-resonance absorbance data for various input laser intensities, which can be obtained with a tunable CW laser without the need for precise frequency locking. We applied this method to measure the effective saturation intensities of all four Doppler-broadened D2 transitions in natural rubidium (Rb) vapour (27.8%87Rb and 72.2 %85Rb{}^{\text{8}} {}^{\text{5}}Rb85Rb) atr=35∘Cr={35}^{\circ} \mathrm{C}r=35∘C. The results show that the effective saturation intensities for Rb range from 0.752 to 16.8W.m−2\mathrm{W}.\mathrm{m}^{-2}W.m−2. Notably, for certain transitions (specifically, repump transitions), the effective saturation intensities were smaller than 16.7 W.m−2\mathrm{m}^{-2}m−2(up to an order of magnitude), with potentially important implications for optical pumping in Doppler-broadened transitions.
In this paper the saturation spectra of rubidium vapour at room temperature, obtained with overlapped co-propagating laser beams, were examined. Unlike the standard saturation spectroscopy, here the transmission of the pump laser beam was detected. The pump laser was locked to an atomic transition of the D2 line, while the probe laser frequency was scanned in a wide frequency range. The pump and probe beams had approximately the same intensities; thus the probe laser can saturate transitions and contribute to optical pumping. This, together with Doppler broadening, leads to rich pump transmission spectra, with many lines appearing due to the interaction of lasers with atoms in different velocity groups. The advantages of this method are well-resolved structures and appearance of spectral lines on a flat, Doppler-free background. Agreement between experimental and theoretical results shows the usefulness of this simple model, based on the rate equations, for identification of lines and determination of relative contribution to the observed line intensity from atoms with different velocities. Theoretical spectra are a useful tool for the calibration of experimental spectra obtained by a nonlinear dependence of the laser frequency on the voltage applied to the piezo used for the laser diode frequency scanning.
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.
The 5S1/2→6P3/25S_{1/2} \rightarrow 6P_{3/2}5S1/2​→6P3/2​ transition of rubidium at 420420420 nm is a promising candidate for a portable warm-vapor all-optical atomic clock. Despite recent precision spectroscopy studies at 420420420 nm in Rb, an experimental determination of the saturation intensity of this transition has not yet been reported. The saturation intensity is a fundamental parameter that influences the identification of a potential clock transition frequency in terms of optimizing various intensity-dependent parameters and connected systematics. In this work, we report the first experimental measurement of the saturation intensity of the 420420420 nm transition in Rb, obtaining (23.18±0.28)(23.18 \pm 0.28)(23.18±0.28) mW/cm2^22 for the 87^{87}87Rb F=2→F′=3F = 2 \rightarrow F' = 3F=2→F′=3 transition and (25.56±0.37)(25.56 \pm 0.37)(25.56±0.37) mW/cm2^22 for the 85^{85}85Rb F=3→F′=4F = 3 \rightarrow F' = 4F=3→F′=4 transition, in excellent agreement with theoretical predictions. We further investigate the temperature dependence of the Doppler-free Lamb-dip amplitude and linewidth over 59.03 ± 0.3759.03~\pm~0.3759.03 ± 0.37 - 91.20 ± 0.90∘91.20~\pm~0.90^\circ91.20 ± 0.90∘C in a 100100100 mm commercial vapor cell, identifying around 82.02 ± 0.73∘82.02~\pm~ 0.73^\circ82.02 ± 0.73∘C as the optimal operating temperature, where the signal-to-noise ratio of the Lamb-dip amplitude with temperature reaches a maximum and the observed Lamb-dip linewidth exhibits a minimum. We also present precise measurements of the magnetic-dipole (AAA) and electric-quadrupole (BBB) hyperfine constants of the 6P3/26P_{3/2}6P3/2​ state for both isotopes, with the measured values being consistent with previously reported values for the hyperfine constants.
We have made systematic studies of rubidium (Rb) number density and polarization with the purpose of comparing a variety of techniques used to make these measurements. We have used five different temperatures, 40°C to 100°C in 15° increments, to compare number density measurements made using optical absorption with those made using Faraday rotation. A diode laser operating in the region near the Rb D1 transition was used in the case of the former, while for the latter two different lasers were used, one each operating in the vicinity of the Rb D1 and D2 transitions. These number density results are compared with those obtained from vapor temperature formulae (e.g., Killian, CRC, etc.). We have also made a systematic study of Rb optical pumping using an amplified tunable diode laser which has been incrementally broadened in order to determine the effect of linewidth broadening on Rb polarization. We vary the frequency of the circularly-polarized pump laser across the D1 transition absorption profile for each of four linewidths (0.01, 0.5, 2, and 8 GHz) and measure the Rb polarization using Faraday rotation. The Rb number density for these measurements is on the order of 1012 cm−3, with 1 Torr of N2 as the buffer gas. These results are then compared with polarization measurements taken using a re-pump laser operating near the Rb D2 transition, and with theoretical calculations of the rubidium polarization.
Zeeman splitting in the D 2 line of rubidium atoms ( 87 Rb and 85 Rb) has been studied using 'Doppler broadened' as well as 'saturation absorption spectroscopy'. While a linearly polarized beam was used for the former experiment, in the latter case a (π, σ ± ) polarization configuration was employed for both pump and probe beams. Zeeman lines have been observed by applying a field up to 5 mT. The field variation of relative line intensities in Doppler-broadened spectrum was determined following Tremblay et al and Nakayama's four-level model. For the saturation spectrum, a four-level model was used. Because the enhancement of absorption at the field is as low as 1 mT, the F g = 2 to F e = 3 transition for 87 Rb can be used as the reference for laser locking. Level crossing is observed in 85 Rb at fields less than 5 mT.
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.