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Physical Review A

Spin-noise spectrum of hot vapor atoms in an anti-relaxation-coated cell

Yuanjiang Tang, Wen Ya, Ling Cang Cai, Kaifeng Zhao

Published Jan 21, 2020• 29 citations
Publisher

Abstract

We study the spin-noise spectrum (SNS) of unpolarized Rb vapor in an evacuated anti-relaxation-coated cell using parametric Faraday rotation of a flat-top probe beam with variable diameter. We identify a distinct structure in the spectrum, called the Ramsey peak. We find that the power of the Ramsey peak is inversely proportional to the total number of atoms in the cell, and the power of the total spin noise is inversely proportional to the number of atoms within the probe beam. We further present a full theoretical analysis of the SNS by comparing three models of spin diffusion: Fickian diffusion, the ballistic flight, and Langevin's diffusion. We find that Fickian diffusion fails, while the ballistic flight is acceptable. However, Langevin's diffusion yields a remarkable agreement with the experimental spectrum.

DOI
10.1103/physreva.101.013821

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We study the spin-noise spectrum (SNS) of unpolarized Rb vapor in an evacuated anti-relaxation-coated cell using parametric Faraday rotation of a flat-top probe beam with variable diameter. We identify a distinct structure in the spectrum, called the Ramsey peak. We find that the power of the Ramsey peak is inversely proportional to the total number of atoms in the cell, and the power of the total spin noise is inversely proportional to the number of atoms within the probe beam. We further present a full theoretical analysis of the SNS by comparing three models of spin diffusion: Fickian diffusion, the ballistic flight, and Langevin's diffusion. We find that Fickian diffusion fails, while the ballistic flight is acceptable. However, Langevin's diffusion yields a remarkable agreement with the experimental spectrum.
We use paramagnetic Faraday rotation to study spin noise spectrum from unpolarized Rb vapor in a tightly focused probe beam in the presence of N2{\mathrm{N}}_{2}N2​ buffer gas. We derive an analytical form for the diffusion component of the spin noise time-correlation function in a Gaussian probe beam. We also obtain analytical forms for the frequency spectrum of the spin noise in the limit of a tightly focused or a collimated Gaussian beam in the presence of diffusion. In particular, we find that in a tightly focused probe beam the spectral line shape can be independent of the buffer gas pressure. Experimentally, we find good agreement between the calculated and the measured spin noise spectra for N2{\mathrm{N}}_{2}N2​ gas pressures ranging from 56 to 820 Torr.
Spin squeezing can suppress quantum projection noise via interparticle entanglement, therefore enabling measurement sensitivities beyond the standard quantum limit. In practice, however, the Gaussian and finite intensity profiles of the optical probe beam induce spatially inhomogeneous atom-light interactions. As polarized atoms move within a vapor cell, they experience position-dependent optical intensities, generating transit noise that limits spin squeezing performance. Here, we investigate the transit noise in a coated rubidium vapor cell through combined theoretical analysis and experimental measurements. By varying the probe beam diameter, we quantify the dependence of transit noise on beam size and atomic Larmor frequency. Our results show that, for a vapor cell with fixed dimensions, the transit noise increases as the probe beam spot area decreases. Moreover, when the Larmor frequency is below the characteristic linewidth of the transit noise, the noise contribution becomes larger. We further calculated and measured spin squeezing for different beam sizes and found an experimental difference of 2.7±0.22.7 \pm 0.22.7±0.2 dB between 2~mm and 0.6~mm, similar to the theoretical prediction of 3.0±0.33.0 \pm 0.33.0±0.3 dB. Theoretical analysis under conditions of stronger squeezing shows that transit noise becomes an even more critical limiting factor. These results provide practical guidance for optimizing probe beam parameters and suppressing transit noise in spin squeezing experiments.
We examine experimentally and theoretically the Ramsey effects on the coherent population trapping (CPT) resonance in a paraffin-coated Rb vapor cell. The observed CPT spectrum in the Hanle configuration of the 5S 1/2(F = 2)−5P 1/2(F′ = 1) transition of 87Rb atoms consists of a narrow structure with a spectral width of 0.10 mG due to the wall-induced Ramsey effect and a broad structure with a spectral width of 23 mG due to the transit effect. Considering the velocity distribution of atoms and the number of wall-atom collisions, we numerically calculated the transmittance of the laser beam as a function of the longitudinal magnetic field. The experimental results of the CPT Ramsey interference were in good agreement with the theoretical results, and the dependences of the CPT Ramsey effects on the atom-laser interaction time were investigated in detail.
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.
Atomic beams are powerful tools for measuring spin coherence in hot vapors but require bulky setups, limiting device miniaturization. We demonstrate that micron-thin vapor cells can mimic atomic beam behavior by exploiting geometry-dependent velocity filtering. In a 5 μm rubidium cell, coherence is preserved for atoms moving parallel to the cell walls, enabling observation of the Faraday-Ramsey effect without buffer gas or anti-relaxation coatings. Using a spatially displaced pump-probe scheme and magnetic field scanning, we achieve clear Ramsey fringes and validate our model experimentally. This technique offers a compact alternative to atomic beam systems, supporting scalable sensors and frequency standards.
We present a detailed experimental and theoretical study of edge enhancement in optically pumped Rb vapor in coated cylindrical pyrex glass cells. The Zeeman polarization of Rb atoms is produced and probed in the vicinity ( ~ ${10}^{\ensuremath{-}4}$ cm) of the cell surface by evanescent pump and probe beams. Spin-polarized Rb atoms diffuse throughout the cell in the presence of magnetic field gradients. In the present experiment the edge enhanced signal from the back surface of the cell is suppressed compared to that from the front surface, due to the fact that polarization is probed by the evanescent wave at the front surface only. The observed magnetic resonance line shape is reproduced quantitatively by a theoretical model and yields information about the dwell time and relaxation probability of Rb atoms on Pyrex glass surfaces coated with antirelaxation coatings.