Alkali Metal Number Density Measurement via Faraday Rotation at Low Magnetic Field
POSTER
Abstract
Precise measurement of the alkali-metal number density [A] in spin-exchange optical pumping (SEOP) vapor cells is important for measuring both the alkali-metal polarization and spin-exchange rate coefficient that characterizes SEOP. Compared to optical absorption spectroscopy [1], Faraday rotation of plane-polarized light is better decoupled from light-intensity variations, is easy to calibrate using a half-wave plate, and does not require a detailed understanding of the resonance line shape or integrated absorption [2–4]. However, the rotation is proportional to applied field and is small (∼10-4 rad/G) in fields typically used for SEOP. Additionally, in 129Xe SEOP alkali-metal densities are lower at typical operating temperatures, resulting in lower SNR.
We present a scheme for measurement of [Rb] in the temperature range 80−140◦C by measuring the Faraday rotation per unit magnetic field θ/B as a function of wavelength-detuning ∆D2 from the D2 resonance where [Rb] ∝ ∆D22 θ/B. To measure θ/B, circularly polarized D2 light is passed through a photo-elastic modulator, then through the cell containing Rb vapor [2], resulting in a signal proportional to the rotation. An AC magnetic field is supplied by a pair of coils concentric with a stable DC field. The 50 kHz signal is demodulated and passed to a second lock-in amplifier referenced to the field-modulation frequency.
Assuming that [Rb] does not change during the measurements, we expect a flat line when plotting [Rb] vs ∆D2. Any wavelength-independent rotation shows up as a parabolic function of ∆D2 and the density [Rb] is extracted as the minimum of a parabolic fit. Although the earliest experimental demonstrations employed fields ≈10kG, we have shown that 3−5% measurements of [Rb] using Faraday rotation are possible in the magnetic field and density regime of Xe SEOP.
[1] Kelley, M.; Branca, R. T. AIP Adv. 2022, 12, 095307.
[2] Chann, B.; et al Phys. Rev. A 2002, 66, 032703.
[3] Vliegen, E.; et al. Nucl. Instrum. Methods Phys. Res. A 2001, 460, 444–450.
[4] Shang, H.; et al J. Phys. D: Appl. Phys. 2022, 55, 335106
We present a scheme for measurement of [Rb] in the temperature range 80−140◦C by measuring the Faraday rotation per unit magnetic field θ/B as a function of wavelength-detuning ∆D2 from the D2 resonance where [Rb] ∝ ∆D22 θ/B. To measure θ/B, circularly polarized D2 light is passed through a photo-elastic modulator, then through the cell containing Rb vapor [2], resulting in a signal proportional to the rotation. An AC magnetic field is supplied by a pair of coils concentric with a stable DC field. The 50 kHz signal is demodulated and passed to a second lock-in amplifier referenced to the field-modulation frequency.
Assuming that [Rb] does not change during the measurements, we expect a flat line when plotting [Rb] vs ∆D2. Any wavelength-independent rotation shows up as a parabolic function of ∆D2 and the density [Rb] is extracted as the minimum of a parabolic fit. Although the earliest experimental demonstrations employed fields ≈10kG, we have shown that 3−5% measurements of [Rb] using Faraday rotation are possible in the magnetic field and density regime of Xe SEOP.
[1] Kelley, M.; Branca, R. T. AIP Adv. 2022, 12, 095307.
[2] Chann, B.; et al Phys. Rev. A 2002, 66, 032703.
[3] Vliegen, E.; et al. Nucl. Instrum. Methods Phys. Res. A 2001, 460, 444–450.
[4] Shang, H.; et al J. Phys. D: Appl. Phys. 2022, 55, 335106
*Funding provided by NSF grant PHY-2110608.
Presenters
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Eleanor Terry-Welsh
- Washington State University