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Advanced Quantum Technologies

Measurement of Rubidium Vapor Density Based on Spin‐Exchange Rate

Huining Shang, Sheng Zou, Hong Zhang, Jiancheng Fang

Published Mar 17, 2024• 4 citations
Publisher

Abstract

Abstract An efficient method is proposed for quantifying rubidium vapor density by analyzing the spin‐exchange rate between alkali metals. This method effectively addresses two primary challenges in measuring alkali vapor density. First, it overcomes the limitation of absorption spectroscopy to measure vapor density under optically thick conditions, typically restricted to temperature higher than 420K, equivalent to alkali vapor density exceeding . Second, it mitigates the risk of disrupting shielding functionality due to the application of a strong magnetic field, often in the range of several tens of Gauss or higher, when employing the Faraday rotation for vapor‐density measurement. The spin‐exchange rate between atoms, inherently related to the vapor density, is evident in the electron‐paramagnetic‐resonance spectrum of spin‐polarized , thereby providing a possibility for measuring alkali vapor density. To eliminate overlap between two Lorentzian curves resulting from two decomposed components of an oscillating field, a small rotating magnetic field with identical amplitude and frequency but a 90‐degree phase shift along both the x and y axes is applied. This method is successfully employed to measure vapor density in the temperature range of 373–433 K, with the measured outcomes closely matching the saturation vapor curve.

DOI
10.1002/qute.202300301

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Abstract An efficient method is proposed for quantifying rubidium vapor density by analyzing the spin‐exchange rate between alkali metals. This method effectively addresses two primary challenges in measuring alkali vapor density. First, it overcomes the limitation of absorption spectroscopy to measure vapor density under optically thick conditions, typically restricted to temperature higher than 420K, equivalent to alkali vapor density exceeding . Second, it mitigates the risk of disrupting shielding functionality due to the application of a strong magnetic field, often in the range of several tens of Gauss or higher, when employing the Faraday rotation for vapor‐density measurement. The spin‐exchange rate between atoms, inherently related to the vapor density, is evident in the electron‐paramagnetic‐resonance spectrum of spin‐polarized , thereby providing a possibility for measuring alkali vapor density. To eliminate overlap between two Lorentzian curves resulting from two decomposed components of an oscillating field, a small rotating magnetic field with identical amplitude and frequency but a 90‐degree phase shift along both the x and y axes is applied. This method is successfully employed to measure vapor density in the temperature range of 373–433 K, with the measured outcomes closely matching the saturation vapor curve.
Abstract The alkali number density inside the sealed vapor cell restricts the fundamental sensitivity of the atomic magnetometer and may decrease in the long term, thus motivating the investigation of an in situ density determination method on atomic magnetometers. This paper presents a method to measure the alkali number density, which is proportional to the spin-exchange relaxation rate, through phase-frequency analysis. The magnetic resonance response of the atomic magnetometer was actively strengthened at low polarization by increasing the oscillating field amplitude. To downplay the side effect of the transverse field broadening, phase-frequency analysis was applied to extract the transverse relaxation time limited by spin-exchange collisions. The experimental results coincided well with the saturated vapor pressure curve ranging from 413 K to 463 K. Calculated densities were approximately 0.779–0.992 times those of predictions. The density measurement accuracy was improved compared to traditional methods.
Abstract The actual vapor density characterizing the alkali metal spin-exchange rate remains a compelling issue for spin-exchange optical pumping. Based on the deduced relationship between the Faraday rotation angle and the rubidium vapor number density using the electrodynamics theory, we report a measurement of the number density for rubidium vapor sealed inside a cell based on a Faraday modulator. The measurement relies on the optical rotation angle due to rubidium vapor under a bias magnetic field (∼0.08 T) produced by a samarium–cobalt magnet. A Faraday modulator with a lock-in amplifier is used to accurately measure the tiny optical rotation angle in a temperature range of 387–468 K. In addition, a synchronization verification is performed by the photoelastic modulator (PEM). The recurring data showed that the two methods are consistent with each other. Compared with the PEM method, the Faraday modulator detection system does not need to adjust the optical axis difference of 45° in the PEM detection system, thereby reducing the complexity of the experiment and the error caused by the alignment of the optical axis, which showed that the Faraday modulator detection method more advantageous in measuring the alkali metal density.
High sensitivity measurements of inertia and magnetic field could be achieved by utilizing a category of devices, which manipulate the atomic spins in the spin-exchange-relaxation-free regime. The alkali cell which contains the alkali metal vapor is used to sense magnetic field and inertia. The atomic number density of alkali vapor and the polarization of alkali metal vapor are two of the most important parameters of the cell. They play an important role in the research on atomic spins in the spin-exchange-relaxation-free regime. Besides, optical polarization plays an important role in quantum computing and atomic physics. We propose a measurement of alkali vapor polarization and alkali number density by detecting the optical rotation in one system. This method simplifies existing experimental equipment and processes. A constant bias magnetic field is applied and the Faraday rotation angle is detected by a bunch of the probe beam to deduce alkali-metal density. Then the magnetic field is closed and a bunch of the pump laser is utilized to polarize alkali-metal. Again, the probe beam is utilized to obtain the polarization of alkali metal. The alkali density obtained at first is used to deduce the polarization. This paper applies a numerical method to analyze the Faraday rotation and the polarization rotation. According to the numerical method, the optimal wavelength for the experiment is given. Finally, the fluctuation of magnetic field and wavelength on signal analysis are analyzed.
This study presents a novel method for measuring the number density of K in K-Rb hybrid vapor cells using circularly polarized pump light on polarized alkali metal atoms. This proposed method eliminates the need for additional devices such as absorption spectroscopy, Faraday rotation, or resistance temperature detector technology. The modeling process involved considering wall loss, scattering loss, atomic absorption loss, and atomic saturation absorption, with experiments designed to identify the relevant parameters. The proposed method is real-time, highly stable, and a quantum nondemolition measurement that does not disrupt the spin-exchange relaxation-free (SERF) regime. Experimental results demonstrate the effectiveness of the proposed method, as the longitudinal electron spin polarization long-term stability increased by 204% and the transversal electron spin polarization long-term stability increased by 44.8%, as evaluated by the Allan variance.
This paper reports measurements to determine the spin-exchange cross section for collisions between like alkali atoms. The spin-exchange cross section is determined for Cs133{\mathrm{Cs}}^{133}Cs133, Rb87{\mathrm{Rb}}^{87}Rb87, Rb85{\mathrm{Rb}}^{85}Rb85, K39{\mathrm{K}}^{39}K39, and Na23{\mathrm{Na}}^{23}Na23. The lifetime of the alkali atoms in the Zeeman sublevels of the ground-state hyperfine levels is dominated by spin-exchange collisions. The spin-exchange collision rate is therefore reflected by the linewidth of the microwave absorption spectrum observed in the magnetic dipole transitions between various of the Zeeman sublevels. The measurements employed an XXX-band electron paramagnetic resonance spectrometer. The alkali metal was distilled into a sample bulb which was placed inside a Dewar in a resonant cavity. The bulb was then heated to a temperature corresponding to an equilibrium vapor density of approximately 1015{10}^{15}1015 alkali atoms/c.c. and the microwave absorption spectrum was recorded. In order to relate the spin-exchange rate to a cross section, it is necessary to determine the alkali density. This was done by comparing the intensity of the alkali EPR absorption to that of a weighed and oriented copper sulfate crystal. For Cs133{\mathrm{Cs}}^{133}Cs133 and Rb87{\mathrm{Rb}}^{87}Rb87, interpretation of the linewidth data is complicated by the fact that the transitions occur in a region where there is appreciable mixing of the high-field spin states by the hyperfine interaction. A density-matrix description of spin exchange which corrects for this intermediate field mixing is discussed, and the corrections are applied to the measured cross sections for two transitions in Cs133{\mathrm{Cs}}^{133}Cs133 and Rb87{\mathrm{Rb}}^{87}Rb87. Relative cross sections, referred to that of Na23{\mathrm{Na}}^{23}Na23, are also given.