Measurement of Rb atomic density with background-free optical absorption method obeying pressure-aligned theoretical modeling

Accurate atomic density measurement is crucial to enhancing the performance of quantum sensors, but empirical formulas may be susceptible to overestimate Rb density and lead to significant discrepancies with direct measurements. To address the challenge of obtaining the number density of Rb atoms in the vapor phase, we present an improved model for Rb atomic density measurement based on a modified saturated vapor pressure approach. Our model integrates the Van der Waals equation with a refined Clausius-Clapeyron formulation, improving agreement by capturing pressure-dependent deviations often overlooked. It explicitly demonstrates a positive correlation between atomic density and buffer gas pressure at a constant temperature. In particular, we experimentally quantify the temperature-dependent variation of internal pressure in sealed vapor cells, and incorporate it into the model to further enhance its theoretical accuracy. To achieve high measurement precision, we developed a background-free optical absorption method with the elimination of integrated background-noise to suppress the interference from cell glass and reflections, and further enhanced the system by employing a dual-beam differential configuration and a stabilized detection baseline to ensure high reproducibility and minimal systematic error. Compared with conventional empirical methods, our proposed model significantly enhances the agreement between theory and experiment by incorporating the buffer gas pressure changing with the temperature, which is experimentally measured with background-free optical absorption, thereby improving the measurement accuracy by 6.2 times.