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Physical Review Letters

Nonlinear Hyperfine Pressure Shift by Optical Pumping with White Light

E. S. Ensberg, G. ZU PUTLITZ

Published Jun 23, 1969• 29 citations
Publisher

Abstract

Optical pumping methods have been extended to high buffer-gas pressures by replacing the customary resonance lamp by a white-light source. Rb ground-state Zeeman transitions were detected by resonance fluorescence at argon buffer-gas pressures up to 23 atm. Hyperfine-transition frequencies were measured at 4170 Torr (0\ifmmode^\circ\else\textdegree\fi{}C) and at 7390 Torr (0\ifmmode^\circ\else\textdegree\fi{}C) and showed the first nonlinear pressure dependence so far observed.

DOI
10.1103/physrevlett.22.1349

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Physical Review A•Oct 1, 1970•23 citations
Optical pumping methods have been extended to high buffer-gas pressures by replacing the customary resonance lamp by a white-light source. Rb ground-state Zeeman transitions were detected by resonance fluorescence at argon buffer-gas pressures up to 23 atm. Hyperfine-transition frequencies were measured at 4170 Torr (0\ifmmode^\circ\else\textdegree\fi{}C) and at 7390 Torr (0\ifmmode^\circ\else\textdegree\fi{}C) and showed the first nonlinear pressure dependence so far observed.
Optical pumping is fundamental to high-precision measurement using thermal alkali-metal atoms in vapor cells. In applications such as atomic magnetometry, buffer gases (e.g., N2\mathrm{N}_2N2​ or He\mathrm{He}He) at specific pressures are introduced to quench fluorescence and mitigate wall relaxation. In the high-pressure limit (e.g., the N2\mathrm{N}_2N2​ pressure pN2>1p_{\mathrm{N}_2}> 1pN2​​>1~atm), where collisional broadening exceeds hyperfine splittings of the atoms, optical pumping theory provides a clear description of the angular momentum exchange between photons and atomic spins. However, in many magnetic sensing scenarios, the high-pressure approximation becomes inadequate as its pressure conditions are not strictly satisfied. Consequently, an explicit description of optical pumping under realistic pressures is critical for selecting operating points and enhancing system performance. To address this, we develop a unified theoretical framework of optical pumping in the quasi-high-pressure regime, where collisional broadening is comparable to the ground-state hyperfine splitting. We demonstrate that light absorption, spin polarization, and magnetic-resonance linewidth in this regime differ significantly from those predicted by the high-pressure limit and offer favorable operating conditions. Our study extends conventional modeling and offers critical guidance for atomic magnetometry operating under realistic buffer gas pressures.
The linewidth and frequency associated with the ground state hyperfine energy fo Rb 87 has been studied. A stable single mode semiconductor laser is used to optically pump Rb, in order to obtain a highly collimated, monochromatic light source. The laser is stabilized by locking its optical frequency to the Rb absorption line center. The dependence of the hyperfine frequency and resonance linewidth have been measured as a function of temperature, light intensity and microwave power; and a theoretical description of the linewidth vs. temperature data is presented. Keywords: Optical pumping; Rubidium; Frequency standard; Frequency shift; Light shift; Density matrix; Buffer gas; Linewidth; and Magnetic resonance.
Pressure shifts of the hyperfine splitting in Na 3(2)S((1/2)) that are due to buffer gases have been measured for the first time to our knowledge by all-optical means using the method of synchronized-quantum-beat spectroscopy reported previously [Y. Fukuda et al., Opt. Commun. 38, 357 (1981)]. The substate coherence is excited and detected with amplitude-modulated mode-locked laser pulses tuned to the D(1) line (pulse-repetition frequency, f(p); modulation frequency, f(m)), and the resonances observed at f(0) = nf(p) + ńf(m), (n and n' are integers) are used for the measurement. The pressure-shift coefficients obtained at 210 degrees C are 82, 61, -1, and -47 Hz/Torr for He, N(2), Ar, and Kr, respectively, within an accuracy of +/-3 Hz/Torr.
For precision atomic magnetometry, inert buffer gas is included in alkali-metal vapor cells to significantly broaden hyperfine transitions, which facilitates optical pumping and reduces diffusive relaxation, while also providing non-radiative excited state quenching. We show low-buffer gas pressure (below 50 Torr) alkali vapor cells with resolved hyperfine manifolds can also yield high-performance magnetometers. For high polarization in 87^{87}87Rb, we optically pump F=2F=2F=2 states with narrow linewidth σ+σ_+σ+​ light, while tuning a probe beam to depopulate F=1F=1F=1 states (Δν=6.8Δν= 6.8Δν=6.8 GHz from F=2F=2F=2). The probe tuning then also provides F=2F=2F=2 detection with high optical rotation and low probe broadening; we demonstrate top-bottom gradiometry, within a single 25 Torr, 0.5 cc cell, that yields an Earth's field free-precession magnetometer sensitivity of 18 fT/Hz\sqrt{\text{Hz}}Hz​ with a 1 kHz bandwidth, as well as RF magnetometer sensitivity of 12 fT/Hz\sqrt{\text{Hz}}Hz​ in a small band about 110 kHz.
Relaxation experiments performed on alkali atoms polarized in their ground state by optical pumping in the presence of a rare gas have been previously reported and interpreted. It was shown that the relaxation governed by the spin-orbit interaction is strongly affected by the formation of chemically unstable Rb-Kr molecules bound by van der Waals forces. The previous theoretical analysis, restricted to the longitudinal relaxation, is extended here to relaxation processes involving the transverse components of the electronic polarization and hyperfine "coherences" (elements of the density matrix between different hyperfine states). The effects resulting from the action of a rf field are also examined. The main results of this work, among others, are (a) the prediction of a Zeeman transition-line pressure shift, in some circumstances larger by several orders of magnitude than the one calculated by Herman, and having a very peculiar variation with the rare-gas pressure; (b) a quantitative explanation of the anomalous pressure dependence of the hyperfine transition linewidth discovered by Bender and Cohen; (c) a proposal of a method of detection of rf transitions between states of the alkali---rare-gas molecules by their effect on the relaxation process.