Ultrastable Optical Magnetometry

Nathanial Wilson, Philip Light, André Luiten, and Christopher Perrella

Phys. Rev. Applied 11, 044034 – Published 11 April 2019

Abstract

We report on an ultrastable optical magnetometer based on nonlinear magneto-optical rotation in ${}^{87}{Rb}$ vapor. The atomic vapor is both optically pumped and probed on the $F = 2 \to F^{'} = 1$ hyperfine transition of the $D_{1}$ manifold. A measurement over 26 h quantifies the magnetometer’s performance across 8 orders of magnitude in the Fourier-frequency domain, allowing us to measure the magnetic response into the microhertz domain. We demonstrate a room-temperature sensitivity floor of 15 ${fT}_{rms} / \sqrt{Hz}$ at a magnetic-field strength of $2.5 μ T$ , which corresponds to a record $9 ppb / \sqrt{Hz}$ fractional sensitivity. The magnetometer’s performance is photon shot-noise limited from 40 Hz to 10 kHz, while below 40 Hz it slowly degrades as approximately $f^{- 1 / 4}$ . At 1 mHz the performance is still better than 1 ${pT}_{rms} / \sqrt{Hz}$ . We show that this worsening performance is not a characteristic of the sensor, but instead associated with minute fluctuations of the magnetic field at the sensor from various identified sources.

Received 19 November 2018
Revised 21 January 2019

DOI:https://doi.org/10.1103/PhysRevApplied.11.044034

Physics Subject Headings (PhySH)

Light-matter interaction Magneto-optical effect Metrology Polarization of light

Alkali metals Atomic gases

Resonance techniques

Atomic, Molecular & Optical

Authors & Affiliations

Nathanial Wilson^*, Philip Light, André Luiten, and Christopher Perrella

Institute for Photonics and Advanced Sensing (IPAS), and School of Physical Sciences,The University of Adelaide, South Australia 5005, Australia

^*nathanial.wilson@adelaide.edu.au

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Vol. 11, Iss. 4 — April 2019

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Images

Figure 1
Simplified experimental setup, showing the external cavity diode laser (ECDL), acousto-optic modulator (AOM), Glan-Thompson prism (GT), Wollaston prism (WP), photodetector (PD), lock-in amplifier (LIA), servo controller (SC), and frequency counter (CNT). The probe beam is shown in blue, while the pump beam is shown in red. All relevant electronic components are referenced to the 10-MHz output of a cesium atomic clock. The AM and FM labels denote amplitude and frequency modulation, respectively.
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Figure 2
In-phase and quadrature components of the AMOR resonance measured using time-averaged pump and probe powers of $P_{pump} = 15 μ$ W and $P_{probe} = 5 μ$ W respectively, with a complex Lorentzian fit using Eq. (2). The quadrature component has an amplitude of $A = 7.57$ mrad, a width of $Γ = 13.4 Hz = 0.96$ nT, and a calculated slope of $S = 1.13$ mrad/Hz using Eq. (3). The resonance is centered around a modulation frequency of $Ω_{m} / 2 π = 34.672$ kHz, corresponding to a magnetic-field strength of $B = 2.4781 μ$ T.
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Figure 3
Optical-power-optimization contour plots for the magnetometer, showing the resonance amplitude $A$ (a), resonance width $Γ$ (b), resonance slope in magnetic units $S γ / π$ (c) and the shot-noise-limited sensitivity $δ B$ (d). The optimum operating point occurs for time-averaged pump and probe powers of $P_{pump} = 15 μ$ and $P_{probe} = 5 μ$ , respectively. Using this combination of optical powers results in a shot-noise-limited sensitivity of $15 {fT}_{rms} / \sqrt{Hz}$ .
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Figure 4
Amplitude spectral density of the magnetometer noise floor (blue trace) calculated via Welch’s method [46], using a 26-h measurement. The noise floor is shot-noise limited (red trace) above 40 Hz, but exhibits excess noise at low Fourier frequencies arising from unwanted fluctuations in the magnetic field at the sensor. In the intermediate frequency range (30 mHz to 40 Hz), Johnson current noise in the solenoid generates magnetic noise (solid purple trace, with a 5-Hz-filtered version shown in the dashed purple trace). Between 1 and 30 mHz, magnetic noise arising from the innermost shield dominates [47] (black trace), while at the lowest frequencies, temperature sensitivity of the solenoid current modulates the magnetic field (green trace). The measured temperature fluctuations of the current source are scaled by an experimentally-determined factor of 100 ${pT/}^{\circ} C$ .
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Figure 5
(a) Free-induction decay measurement performed in the temporal domain, with a carrier frequency of $Ω_{L} / π = 29.567$ kHz and a small sinusoidal frequency modulation at 500 Hz. Dashed black lines highlight the damped exponential envelope, which has a time constant of 14.5 ms. (b) Fourier transform of the free-induction decay data presented in (a), showing a peak at the carrier frequency of $29.567$ kHz (indicated by the dashed vertical line), and both first- and second-order sidebands arising from the sinusoidal modulation at 500 Hz.
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