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American Journal of Physics

The role of hyperfine pumping in multilevel systems exhibiting saturated absorption

David A. Smith, Ifan G. Hughes

Published Apr 13, 2004• 165 citations
Publisher

Abstract

We study pump–probe spectroscopy of Rb vapor. Absorption spectra are presented for a weak probe beam in a room temperature vapor subject to a strong counter propagating pump beam of identical frequency. The importance of hyperfine pumping in the formation of the sub-Doppler spectrum is explained. For typical experimental parameters we clarify why the standard designation of “saturated absorption” spectroscopy is a misnomer. In contrast to saturated absorption, the details of the transient solution are crucial and hyperfine pumping leads to a modification of the absorption for detunings of many tens of natural linewidths from resonance.

DOI
10.1119/1.1652039

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Journal of Physics B Atomic Molecular and Optical Physics•Jul 5, 2022•16 citations
We study pump–probe spectroscopy of Rb vapor. Absorption spectra are presented for a weak probe beam in a room temperature vapor subject to a strong counter propagating pump beam of identical frequency. The importance of hyperfine pumping in the formation of the sub-Doppler spectrum is explained. For typical experimental parameters we clarify why the standard designation of “saturated absorption” spectroscopy is a misnomer. In contrast to saturated absorption, the details of the transient solution are crucial and hyperfine pumping leads to a modification of the absorption for detunings of many tens of natural linewidths from resonance.
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 have shown earlier that hyperfine spectroscopy in a vapor cell using co-propagating pump-probe beams has many advantages over the usual technique of saturated-absorption spectroscopy using counter-propagating beams. The main advantages are the absence of crossover resonances, the appearance of the signal on a flat (Doppler-free) background, and the higher signal-to-noise ratio of the primary peaks. Interaction with non-zero-velocity atoms causes additional peaks, but only one of them appears within the primary spectrum. We first illustrate the advantages of this technique for high-resolution spectroscopy by studying the D2D_2D2​ line of Rb. We then use an acousto-optic modulator (AOM) for frequency calibration to make precise hyperfine-interval measurements in the first excited P3/2P_{3/2}P3/2​ state of 85,87^{85,87}85,87Rb and 133^{133}133Cs.
Laser spectroscopy experiments are often conducted with a probe that does not significantly alter the medium’s properties. For a two-level atom a clear measure of the strength of a probe beam in terms of the saturation intensity is known. We show that for a multilevel atom the situation is very different, and the effects of optical pumping are crucial to understanding the opacity of the medium. We present a simple theoretical analysis for Doppler-broadened spectroscopy of alkali metals on the D2 line that emphasizes the importance of the transient nature of the population dynamics, and the crucial role of the distribution of the times of flight of atoms through the probe beam. Experimental results are obtained with room temperature rubidium vapor probed by an extended-cavity diode laser and confirm our theoretical prediction.
The goal of this experiment was to measure the hyperfine energy splittings of the ground to first excited state transitions in rubidium using saturated absorption spectroscopy. Using this technique, we measured these transition energy spectra by taking the difference of two photodiode outputs due to multiple beams of a single laser scanned over a range of frequencies and shone through a cell of Rb vapor. When the laser frequency was resonant with an atomic transition, photons of those frequencies were absorbed, leaving a dip in intensity of the beam measured at the photodiode. One of the two laser beams had its excitations saturated by a more intense, counter-propagating pump beam from the same laser. The pump beam saturated the absorption of the velocity equal zero atoms that the counter-propagating probe beam could have also interacted with due to no Doppler shift. At these frequencies the probe beam experienced less absorption that was measured by a photodiode. The photodiode output was calibrated to the change in frequency of the scanned laser using a Fabry-Pérot interferometer. The output of this interferometer served as a reference for how the laser frequency changed. Final results for the 87Rb F=1 spectrum accounted for the largest error with a maximum of 12.2% deviation from accepted energy spacing values due in part to systematic error. Other spectra measurements were in better agreement, possessing error ranging from 2.1% to 10.1% and some agreeing with accepted values to within our uncertainty.
We experimentally study the absorption spectroscopy from a collection of gaseous 87Rb^87 Rb87Rb atoms at room temperature irradiated with three fields. Two of these fields are in a pump probe saturation absorption configuration. The third field co-propagates with the pump field. The three fields address Zeeman degenerate transitions between hyperfine levels 5S1/2,F=15S_{1/2}, F = 15S1/2​,F=1 and 5P3/2,F=05P_{3/2}, F = 05P3/2​,F=0 and also between 5S1/2,F=15S_{1/2}, F = 15S1/2​,F=1 and 5P3/2,F=15P_{3/2}, F =15P3/2​,F=1 around the D2 line. We find a sub-natural absorption resonance in the counter-propagating probe field. The novel feature of this absorption is its abrupt onset in the vicinity of 5P3/2,F=05P_{3/2}, F = 05P3/2​,F=0, as the laser frequency is scanned from 5P3/2,F=05P_{3/2}, F = 05P3/2​,F=0 to 5P3/2,F=15P_{3/2}, F =15P3/2​,F=1. The experimental results are compared with the theory modeled after a four level system. There is a qualitative agreement between our theory and experiment. We find the threshold absorption to be a result of the off-resonant interaction of the strong field with nearby hyperfine levels.
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.