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American Journal of Physics

How weak is a weak probe in laser spectroscopy?

Benjamin E. Sherlock, Ifan G. Hughes

Published Jan 12, 2009• 72 citations
Publisher

Abstract

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.

DOI
10.1119/1.3013197

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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 relative intensities of the Doppler-free signals of 85Rb and Cs D2 lines in saturation spectroscopy were calculated theoretically, taking into account the optical pumping process in a four-level system. The optical pumping effect in saturation spectroscopy is important when atoms with long-lived lower states are pumped by a weak beam. The theoretical results calculated from a simple analysis without any knowledge of the saturation parameters were found to be in good agreement with the experimental results on Rb and Cs D2 lines previously obtained using semiconductor laser.
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.
Abstract Laser spectroscopy of hot atomic vapours has been studied extensively. Theoretical models that predict the absolute value of the electric susceptibility are crucial for optimising the design of photonic devices that use hot vapours, and for extracting parameters, such as external fields, when these devices are used as sensors. To date, most of the models developed have been restricted to the weak-probe regime. However, fulfilling the weak-probe power constraint may not always be easy, desired or necessary. Here we present a model for simulating the spectra of alkali-metal vapours for a variety of experimental parameters, most distinctly at intensities beyond weak laser fields. The model incorporates optical pumping effects and transit-time broadening. We test the performance of the model by performing spectroscopy of 87Rb in a magnetic field of 0.6 T, where isolated atomic resonances can be addressed. We find very good agreement between the model and data for three different beam diameters and a variation of intensity of over five orders of magnitude. The non-overlapping absorption lines allow us to differentiate the saturation behaviour of open and closed transitions. While our model was only experimentally verified for the D2 line of rubidium, the software is also capable of simulating spectra of rubidium, sodium, potassium and caesium over both D lines.
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.
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 study the influence of optical pumping on Doppler-broadened alkali-metal-atom DDD line spectra by solving the time-dependent density matrix for an open two-level system. The time-dependent absorption is averaged over the distribution of interaction times obtained from the three-dimensional beam geometry and atomic velocity distribution and over the longitudinal velocity distribution. The optical pumping is significant at much lower intensities than saturation and depends strongly on the intensity, beam radius, vapor cell length, and spontaneous-decay branching ratio. The result is in agreement with our earlier steady-state solution for a wide range of parameters and predicts two interesting line-shape features.