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Physical Review A

Langevin approach to magnetic-field-gradient-induced spin relaxation in a coated cell

Junhe Zheng, Wei Xiao, Sheng Li, Xiang Peng, Teng Wu, Hong Mei Guo

Published Feb 7, 2024• 10 citations
Publisher

Abstract

Magnetic-field-gradient-induced spin polarization transverse relaxation is re-examined in an alkali-metal atomic cell with antirelaxation coating. The experimentally observed motional-narrowing effect in a paraffin-coated vapor cell, a phenomenon for depicting the suppression of spin polarization transverse relaxation caused by the magnetic-field gradient, is more than an order of magnitude weaker than theoretical predictions. Such a discrepancy is due to the existence of background gas. By taking the background gas into consideration, Redfield theory combined with the Langevin approach is proposed to depict the magnetic-field-gradient-induced spin relaxation in a coated cell, and the model is verified to be consistent with the previous results derived under two limits in which the mean free path is either much smaller (diffusion regime) or much larger than (ballistic regime) the cell size. Our work provides a potentially feasible method to evaluate the background gas pressure inside the coated cell, and it can help to foster better comprehension of the performance of an antirelaxation coated cell.

DOI
10.1103/physreva.109.022803

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Magnetic-field-gradient-induced spin polarization transverse relaxation is re-examined in an alkali-metal atomic cell with antirelaxation coating. The experimentally observed motional-narrowing effect in a paraffin-coated vapor cell, a phenomenon for depicting the suppression of spin polarization transverse relaxation caused by the magnetic-field gradient, is more than an order of magnitude weaker than theoretical predictions. Such a discrepancy is due to the existence of background gas. By taking the background gas into consideration, Redfield theory combined with the Langevin approach is proposed to depict the magnetic-field-gradient-induced spin relaxation in a coated cell, and the model is verified to be consistent with the previous results derived under two limits in which the mean free path is either much smaller (diffusion regime) or much larger than (ballistic regime) the cell size. Our work provides a potentially feasible method to evaluate the background gas pressure inside the coated cell, and it can help to foster better comprehension of the performance of an antirelaxation coated cell.
Abstract The spin polarization and spatial homogeneity of alkali metal atoms are critical characteristics that determine the performance of spin-exchange relaxation-free magnetometers. In buffer gas cells, these characteristics are influenced by optical broadening and alkali atomic motional restriction imposed by the buffer gas. In coated cells, the protective effect of the coating on atomic spins, combined with rapid atomic diffusion, leads to significantly superior spin polarization characteristics compared to those in high-pressure buffer gas cells. However, due to neglecting the influence of atom-coating interactions on atomic motion, the existing spin polarization and spatial distribution models fail to accurately describe the polarization characteristics in coated cells. In this paper, based on the Langevin–Bloch equation, a dynamic model considering interaction effects between alkali metal atoms and the coating as well as between the pump light and the hyperfine levels of alkali metal atoms is proposed to accurately describe the spin polarization and spatial distribution in coated cells. To validate the proposed model, a series of experiments were carried out. The results demonstrate that coated cells can maintain high spin polarization and spatial homogeneity even under conditions of low pump intensity and high temperature, which are in good agreement with the simulations. This work provides a theoretical reference for the design of high-performance and low-power quantum sensors.
An alkene-based antirelaxation coating for alkali-metal vapor cells exhibiting Zeeman relaxation times up to 77 s was recently identified by Balabas et al. The long relaxation times, two orders of magnitude longer than in paraffin- (alkane-) coated cells, motivate revisiting the question of what the mechanism is underlying wall-collision-induced relaxation and renew interest in applications of alkali-metal vapor cells to secondary frequency standards. We measure the width and frequency shift of the ground-state hyperfine $m{}_{F}=0\ensuremath{\rightarrow}m{}_{F}^{\ensuremath{'}}=0$ transition (clock resonance) in vapor cells with 85{}^{85}85Rb and 87{}^{87}87Rb atoms, with an alkene antirelaxation coating. We find that the frequency shift is slightly larger than for paraffin-coated cells and that the Zeeman linewidth scales linearly with the hyperfine frequency shift.
This letter reports light narrowing in paraffin-coated vapor cells from room temperature 27℃ to 59℃, where spin-exchange relaxation is suppressed. By means of a coating lock and eliminating the reservoir effect, an ultra-narrow magnetic resonance linewidth of 0.36 Hz and an atomic coherence lifetime of T₂ = 0.9 s are achieved. In cells free of buffer gas, the narrow linewidth over this broad temperature range is a result of enhanced spin polarization, which is facilitated by the effective suppression of radiation trapping benefiting from the stability of the vapor density. Using such cells in atomic magnetometers, the photon shot noise limit is estimated as 0.2 fT/rtHz and the spin-projection noise limit is estimated as 1.1 fT/rtHz. Also, a magnetometer system with the stable coated cell is identified, which demonstrates the potential for achieving relatively stable magnetometer sensitivity without precisely controlling the cell temperature. The long coherence lifetime and broad operating temperature range expand the potential applications of quantum memory and other quantum sensors such as atomic clocks.
We measured the rate of velocity-changing collisions (VCCs) between alkali atoms and background gas in buffer-gas-free anti-spin-relaxation-coated cells. The average VCC rate in paraffin-coated rubidium vapor cells prepared in this work was 1×1061 \times 10^{6}1×106 s−1^{-1}−1, which corresponds to $\sim$1 mm in the mean free path of rubidium atoms. This short mean free path indicates that alkali atoms do not travel freely between the cell walls. In addition, we found that a heating process known as increases the VCC rate, and also confirmed that ripening improves the anti-relaxation performance of the coatings.
Alkali-metal vapor cells with antirelaxation coating (especially paraffin-coated cells) have been a central tool in optical pumping and atomic spectroscopy experiments for 50 years. We have discovered a dramatic change of the alkali-metal vapor density in a paraffin-coated cell upon application of an electric field to the cell. A systematic experimental characterization of the phenomenon is carried out for electric fields ranging in strength from 0--8 kV/cm for paraffin-coated cells containing rubidium and cells containing cesium. The typical response of the vapor density to a rapid (duration $\ensuremath{\lesssim}100\text{ }\text{ms}$) change in electric field of sufficient magnitude includes (a) a rapid (duration of $\ensuremath{\lesssim}100\text{ }\text{ms}$) and significant increase in alkali-metal vapor density followed by (b) a less rapid (duration of $\ensuremath{\sim}1\text{ }\text{s}$) and significant decrease in vapor density (below the equilibrium vapor density), and then (c) a slow (duration of $\ensuremath{\sim}100\text{ }\text{s}$) recovery of the vapor density to its equilibrium value. Measurements conducted after the alkali-metal vapor density has returned to its equilibrium value indicate minimal change (at the level of $\ensuremath{\lesssim}10%$) in the relaxation rate of atomic polarization. Experiments suggest that the phenomenon is related to an electric-field-induced modification of the paraffin coating.