Direct determination of atomic number density in MEMS vapor cells via single-pass absorption spectroscopy (SPAS)

TL;DR

This paper introduces a direct, validated method using single-pass absorption spectroscopy to accurately measure rubidium atom density in MEMS vapor cells, aiding the development of quantum sensors.

Contribution

It presents a novel quantitative approach combining experimental spectra and a detailed theoretical model for atomic density measurement in MEMS vapor cells.

Findings

Model achieves >99% agreement with experimental spectra.

Method is validated across various temperatures, laser intensities, and cell lengths.

Extracted densities align with empirical vapor-pressure models.

Abstract

Micro-electro-mechanical systems (MEMS)-based chip-scale alkali vapor cells are the essential components in emerging quantum technologies, including compact atomic clocks, chip-scale magnetometers, and miniature quantum opto-electronic systems. The sensitivity of MEMS-based atomic quantum technology devices depends on the atomic number density. Thus, it is important to have an accurate estimate of the atomic number density in chip-scale alkali vapor cells to optimize light-matter interactions and design efficient quantum sensing systems. Here, we present a direct and quantitatively validated method for determining the rubidium (Rb) number density in warm alkali vapor using single-pass absorption spectroscopy (SPAS). The absolute transmission spectra are measured and modeled using the 780.24~nm as well as the 420.29~nm transition in a Rb-filled MEMS vapor cell. The atomic number density measurements and the model were also validated using a commercial vapor cell of length 100~mm. The theoretical model employs a density-matrix formalism within the Lindblad framework and incorporates directly measurable experimental parameters, such as laser beam power, diameter, and cell temperature. The model explicitly accounts for optical pumping, Doppler broadening, and transit-time broadening effects and exhibits quantitative agreement ($> 99\%$) with experimental spectra over a broad range of temperatures (293--343~K), laser intensities ($\sim0.2\, I_{\mathrm{sat}}$ to $\sim2\, I_{\mathrm{sat}}$), and cell lengths (2--100~mm). The extracted densities from the MEMS cell closely follow the empirical vapor-pressure model by Alcock et al. The demonstrated methodology provides a practical, well-controlled method for determining the atomic number density in alkali vapor cells relevant to the characterization and development of compact alkali-vapor-based devices for quantum sensing and metrology.