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arXiv:2511.00526

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

Sumit Achar, Sinha, Shivam, M Ezhilarasan, R Chandankumar, Arijit Sharma

Published Nov 1, 2025• 0 citations
arXivHTMLPDF

Abstract

Micro-electro-mechanical systems (MEMS)-based (chip-scale) alkali vapor cells are key components in emerging quantum technologies, where device performance critically depends on the atomic number density. Thus, it is important to have an accurate estimate of the atomic number density in MEMS-based alkali vapor cells to optimize light-matter interactions and design efficient quantum sensing systems. Here, a quantitatively validated method is presented for determining the rubidium (Rb) atomic number density in warm vapor using Single-Pass Absorption Spectroscopy (SPAS). The absolute transmission spectra are measured and modeled using the 780.24~nm and 420.29~nm transitions in Rb-filled MEMS vapor. 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 (293-353~K), laser probe powers of approximately 10~$μ$W-100~$μ$W at the 780.24~nm transition and 8~$μ$W-80~$μ$W at the 420.29~nm transition, and cell lengths (2--100~mm). This method demonstrates a practical and reliable approach for determining the density of alkali vapor cells for quantum sensing, metrology, and quantum communication applications.

DOI
10.48550/arxiv.2511.00526

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Micro-electro-mechanical systems (MEMS)-based (chip-scale) alkali vapor cells are key components in emerging quantum technologies, where device performance critically depends on the atomic number density. Thus, it is important to have an accurate estimate of the atomic number density in MEMS-based alkali vapor cells to optimize light-matter interactions and design efficient quantum sensing systems. Here, a quantitatively validated method is presented for determining the rubidium (Rb) atomic number density in warm vapor using Single-Pass Absorption Spectroscopy (SPAS). The absolute transmission spectra are measured and modeled using the 780.24nm and 420.29nm transitions in Rb-filled MEMS vapor. 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%> 99\%>99%) with experimental spectra over a broad range of temperatures (293-353K), laser probe powers of approximately 10μμμW-100~μμμW at the 780.24nm transition and 8μμμW-80~μμμW at the 420.29nm transition, and cell lengths (2--100mm). This method demonstrates a practical and reliable approach for determining the density of alkali vapor cells for quantum sensing, metrology, and quantum communication applications.
The microfabricated alkali atomic vapor cells are essential for the chip scale quantum sensing instruments which provide a robust, simple platform for precision measurement for a quantum system. In order to solve the problems of difficult quantitative filling of alkali atoms and poor hermeticity in the fabricated process of the cells, the preparation of microfabricated alkali atomic vapor cells with good hermeticity is studied. The cells are fabricated by the microelectromechanical system (MEMS) technology. Rubidium (Rb) atomic vapor cells with nitrogen (N 2 ) as buffer gas are successfully obtained by photolysis of rubidium azide (RbN 3 ), which is confirmed by the presence of Rb vapor in the cells through absorption spectroscopy for the 5S 1/2 → 5P 3/2 and 5S 1/2 → 5P 1/2 transitions in Rb atoms at 780 nm and 795 nm. The influences of filling amount and baking temperature of RbN 3 solution on the hermeticity of the microfabricated atomic vapor cells are demonstrated. Also, the influences of filling amount of Rb atoms and temperature on the absorption spectrum intensities of Rb vapor in the cells are studied through a theoretical analysis. This research provides a reference for the design and preparation of high quality microfabricated alkali atomic vapor cells.
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Rubidium atomic systems are widely employed in quantum precision measurement. As a core component of numerous quantum sensors, the rubidium vapor cell plays a critical role in determining sensitivity and long-term stability of these devices. However, conventional filling techniques remain inadequate for achieving precise quantitative control of rubidium atoms within the vapor cells. In this work, a precise quantitative filling method of rubidium atoms into vapor cells driven by a zoned temperature gradient is proposed. By constructing a multizone temperature field that decreases monotonically from high to low temperatures under a high vacuum condition, directional vapor transport of rubidium atoms is realized. Experimental results demonstrate that the temperature dependence of the atomic number density agrees well with predictions of the empirical model, while the total atomic mass loss is maintained below 10%. These results confirm the validity of the filling method, providing both theoretical support and experimental basis for the scalable fabrication of high-consistency vapor cells for quantum sensing applications.
The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale MEMS cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing excellent quantitative agreement. A Kerr nonlinear refractive index n2n_2n2​ of up to 10−410^{-4}10−4 cm2^22/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.
Microfabricated (MEMS) alkali vapor cells are at the core of high-precision integrated atomic quantum sensors and devices [1], such as microwave and optical clocks, or magnetometers. The first chip-scale atomic device was a microwave atomic clock based on coherent population trapping [2]. It has offered in its industrial and commercialized version an ultra-low size-power -instability budget, impacting a plethora of industrial and scientific applications. Nevertheless, the short-term stability of these clocks is usually limited at about 10−10 at 1 s. Hot vapor MEMS-based optical frequency standards constitute a new generation of miniaturized clocks, with enhanced stability. These references keep the benefit of using wafer-scalable and mass-producible vapor cells while preventing ultra-high vacuum technologies and laser cooling. Among the transitions explored, the 6S1/2 → 7P1/2 near-UV transition of Cs atom was used to demonstrate an optical reference with a stability of 2.1 × 10−13 at 1 s and averaging down to a few 10−14 [3]. However, this reference was based on a 5 cm-long glass-blown cell, not compliant with the advent of a fully-miniaturized and low-power optical clock. In this work [4], we present the characterization of sub-Doppler resonances detected in a microfabricated cell by probing, in a simple saturated absorption configuration, the Cs atom 6S1/2 → 7P1/2 transition at 459 nm. The impact of the laser intensity and cell temperature on the sub-Doppler resonance is experimentally investigated. Optimal values are identified for the development of a near-UV microcell-stabilized frequency reference. Detection noise measurements are also reported, predicting a short-term stability in the 10−13 range at 1 s. Tests of cells with embedded getters are under progress for improved purity of the cell inner atmosphere and narrowing of the resonance.
Accurate characterization of atomic vapor cells is crucial for enhancing the sensitivity of miniature atomic magnetometers. In this study, a fast and efficient approach is developed to characterize relaxation properties of the inner surface of the 87Rb micro-electro-mechanical systems (MEMS) vapor cell. Based on the zero-field level crossing effect, the transverse relaxation rate was experimentally determined, and the depolarization coefficient of 0.097 for atom-wall collisions in the 87Rb MEMS vapor cell was obtained. The experiments demonstrated that the alkali-wall collision relaxation gradually dominates the depolarization of the 87Rb ensemble as the radius of the vapor cell decreases. This research provides a quantitative method to evaluate the effectiveness of the MEMS vapor cell anti-relaxation coatings and offers the design inspiration for MEMS atomic vapor cells from the perspective of relaxation characterization. It is beneficial for the development of weak magnetic field detections such as biomagnetism detection in ambient environments.