We propose and demonstrate pump-probe spectroscopy of rubidium absorption which reveals the sub-Doppler hyperfine structure of the ${}^5$S${}_{1/2}\leftrightarrow$ ${}^5$P${}_{3/2}$ (D2) transitions. The counter propagating 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 which 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 allowed us to extract the number density and temperature of the Rb vapor from the two-dimensional spectrum. In the future this technique could could be used as an atomic frequency standard for calibrating and characterising a single-photon or low-light-level source.

中文翻译：

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-的单光子级亚多普勒泵浦-探针光谱

我们提出并证明了absorption吸收的泵浦探针光谱学，揭示了the的亚多普勒超细结构。 ${}^5$小号${}_{\mathrm{1个}/2}\leftrightarrow$ ${}^5$P${}_{3/2}$（D2）转换。反向传播泵浦和探针激光器的频率可独立调节，探针工作在单光子级。扫描激光频率时测得的二维光谱显示出荧光，多普勒增宽的吸收倾角和亚多普勒特征。泵浦激光器和探测激光器之间的失谐可以补偿室温蒸气中所有原子速度的多普勒频移，这意味着我们观察到光束中所有原子的亚多普勒特征。我们详细介绍了包含荧光，饱和效应和光泵浦的系统理论模型，并将其与测得的光谱进行比较，得出平均绝对百分比误差为3.11％。这种高度的一致性使我们能够从二维光谱中提取Rb蒸气的数量密度和温度。将来，该技术可以用作校准和表征单光子或弱光源的原子频率标准。