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Physical Review Applied

Unambiguous measurement in an unshielded microscale magnetometer with sensitivity below 1 pT / Hz

Hamish A. M. Taylor, Christopher C. Bounds, Alex Tritt, Lincoln D. Turner

Published Aug 16, 2024• 8 citations
Publisher

Abstract

Cold-atom magnetometers exploit a dense ensemble of quanta with long coherence times to realize leading sensitivity on the micrometer scale. Configured as a Ramsey interferometer, a cold-atom sensor can approach atom shot-noise limited precision but suffers from fringe ambiguity, producing gross errors when the field falls outside a narrow predefined range. We describe how Hilbert-demodulated optical magnetometry can be realized on cold-atom sensors to provide field measurements both precise and unambiguous. Continuous reconstruction of the Larmor phase allows us to determine the dc magnetic field unambiguously in an unshielded environment, as well as measure ac variation of the field, in a single shot. The ac measurement allows us to characterize, and then neutralize, line-synchronous magnetic interference, extending reconstruction times. Using $1.6\ifmmode\times\else\texttimes\fi{}{10}^{6}{\phantom{\rule{0.2em}{0ex}}}^{87}\mathrm{Rb}$ atoms in a volume of $(68\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}{)}^{3}$, we measure a test field to be $86.0121261(4)\phantom{\rule{0.1em}{0ex}}\phantom{\rule{0.1em}{0ex}}\text{\ensuremath{\mu}}\mathrm{T}$ in a single shot, achieving dc sensitivity of $380\phantom{\rule{0.1em}{0ex}}\mathrm{fT}$ in a duration of $1000\phantom{\rule{0.1em}{0ex}}\mathrm{ms}$. Our results demonstrate that Hilbert-demodulated optical readout yields metrologically significant sensitivity without the fringe ambiguity inherent to Ramsey interferometry.

DOI
10.1103/physrevapplied.22.024047

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Cold-atom magnetometers exploit a dense ensemble of quanta with long coherence times to realize leading sensitivity on the micrometer scale. Configured as a Ramsey interferometer, a cold-atom sensor can approach atom shot-noise limited precision but suffers from fringe ambiguity, producing gross errors when the field falls outside a narrow predefined range. We describe how Hilbert-demodulated optical magnetometry can be realized on cold-atom sensors to provide field measurements both precise and unambiguous. Continuous reconstruction of the Larmor phase allows us to determine the dc magnetic field unambiguously in an unshielded environment, as well as measure ac variation of the field, in a single shot. The ac measurement allows us to characterize, and then neutralize, line-synchronous magnetic interference, extending reconstruction times. Using 1.6\ifmmode×\else\texttimes\fi10687Rb1.6\ifmmode\times\else\texttimes\fi{}{10}^{6}{\phantom{\rule{0.2em}{0ex}}}^{87}\mathrm{Rb}1.6\ifmmode×\else\texttimes\fi10687Rb atoms in a volume of (68\ensuremath\mum)3(68\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}{)}^{3}(68\ensuremath\mum)3, we measure a test field to be 86.0121261(4)\ensuremath\muT86.0121261(4)\phantom{\rule{0.1em}{0ex}}\phantom{\rule{0.1em}{0ex}}\text{\ensuremath{\mu}}\mathrm{T}86.0121261(4)\ensuremath\muT in a single shot, achieving dc sensitivity of 380fT380\phantom{\rule{0.1em}{0ex}}\mathrm{fT}380fT in a duration of 1000ms1000\phantom{\rule{0.1em}{0ex}}\mathrm{ms}1000ms. Our results demonstrate that Hilbert-demodulated optical readout yields metrologically significant sensitivity without the fringe ambiguity inherent to Ramsey interferometry.
Cold atom magnetometers exploit a dense ensemble of quanta with long coherence times to realise leading sensitivity on the micrometer scale. Configured as a Ramsey interferometer, a cold atom sensor can approach atom shot-noise limited precision but suffers from fringe ambiguity, producing gross errors when the field falls outside a narrow predefined range. We describe how Hilbert-demodulated optical magnetometry can be realised on cold atom sensors to provide field measurements both precise and unambiguous. Continuous reconstruction of the Larmor phase allows us to determine the dc magnetic field unambiguously in an unshielded environment, as well as measure ac variation of the field, in a single shot. The ac measurement allows us to characterize, and then neutralise, line-synchronous magnetic interference, extending reconstruction times. Using 1.6×1061.6 \times 10^61.6×106 87^{87}87Rb atoms in a volume of (68 μm)3(68 \,\mathrm{μm})^3(68μm)3, we measure a test field to be $ 86.0121261(4) \; \mathrm{μT}$ in a single shot, achieving dc sensitivity of 380 fT in a duration of 1000 ms. Our results demonstrate that Hilbert-demodulated optical readout yields metrologically-significant sensitivity without the fringe ambiguity inherent to Ramsey interferometry.
Atoms in magnetically sensitive sublevels constitute a natural sensor for absolute magnetic field measurements, which are explored here to form an optical Ramsey interferometer for determining the magnetic field distribution. An optical Ramsey atom interferometer provides a convenient way to map a magnetic field in vacuum. In comparison with the often used Raman spectroscopy method, a Ramsey interferometer can not only improve the sensitivity, but also dramatically suppress the contribution of the ac Stark effect. Furthermore, in this work, the magnetically sensitive atoms are velocity-selected, which improves the spatial resolution for the magnetometer as well as the contrast of the Ramsey fringes. A short-term sensitivity of 1.4nT/Hz1/21.4\phantom{\rule{0.2em}{0ex}}{\mathrm{nT/Hz}}^{1/2}1.4nT/Hz1/2 for magnetic field measurement is finally achieved even with an interrogation time as short as $500\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$. The presented approach for absolute magnetic field measurement is expected to find wide applications in atom-interferometry-based precision measurements.
Cold-atom magnetometers can achieve an exceptional combination of superior sensitivity and high spatial resolution. One key challenge that these quantum sensors face is improving the sensitivity within a given timeframe while preserving a high dynamic range. Here, we experimentally demonstrate an adaptive entanglement-free cold-atom magnetometry with both superior sensitivity and high dynamic range. Using a tailored adaptive Bayesian quantum estimation algorithm designed for Ramsey interferometry using coherent population trapping (CPT), cold-atom magnetometry facilitates adaptive high-precision detection of a dc magnetic field with high dynamic range. Through implementing a sequence of correlated CPT-Ramsey interferometry, the sensitivity significantly surpasses the standard quantum limit with respect to total interrogation time. We yield a sensitivity of 6.8 ± 0.1 picotesla per square root of hertz over a range of 145.6 nanotesla, exceeding the conventional frequentist protocol by 3.3 ± 0.1 decibels. Our study opens avenues for the next generation of adaptive cold-atom quantum sensors, wherein real-time measurement history is leveraged to improve their performance.
Magnetic field sensing utilizing Bose-condensed atomic gases can achieve both high sensitivity and spatial resolution. Employing two-photon transitions from F=1, mF=1→F=2, mF=-1 (F is the quantum number of total atomic angular momentum, mF is the magnetic quantum number of F level) of Bose-condensed 87Rb atomic gases in one-dimensional optical lattice, the precision magnetic field measurement with phase Ramsey interference has been demonstrated. Utilizing single-photon transitions from F=1, mF=1→F=2, mF=0 of Bose-condensed 87Rb atomic gases in a crossed optical dipole trap, we experimentally study frequency domain Ramsey interference, time domain Ramsey interference, and phase domain Ramsey interference. Based on phase Ramsey interference, the sensitivity and spatial resolution of static magnetic field measurement are evaluated. The comparison of these three typical Ramsey interferences reveals that phase Ramsey interference can effectively avoid the fringe distortion in frequency-domain interference and the decoherence effects in time-domain interference, thereby improving the sensitivity and accuracy of the static magnetic field measurement. Utilizing Bose-condensed 87Rb atomic gases with the volume of 1.31±0.03×10-9 cm3 in an unshielded environment, a sensitivity of 130 nT/Hz for static magnetic fields can be achieved. By reducing the preparation time of the atomic gases and increasing the signal interrogation time, the sensitivity has the potential to be further improved.
This thesis presents advancements in radio-frequency atomic magnetometry utilising cold atoms as sensors. While cold atom magnetometers demonstrate lower absolute sensitivity compared to conventional vapour cell systems due to reduced atom numbers, they offer exceptional spatial resolution at the micrometre scale. The experimental apparatus features a cold atom production system capable of reaching quantum degeneracy through a refined cooling sequence that involves optical molasses, magnetic trapping and evaporation, and optical evaporative cooling in the dipole trap, culminating in a 87Rb Bose-Einstein condensate. This work details the development and characterisation of magnetometer set-ups with progressively enhanced performance. The first magnetometer utilised atoms in the optical molasses phase as a sensor, achieving an AC sensitivity of 330 pT/√Hz with approximately 108 atoms at 20 μK. Comprehensive magnetometry optimisation methods were developed to enhance sensitivity. Following laboratory interruptions due to the COVID-19 pandemic, system rebuilding incorporated significant upgrades, including a new probe laser and gradient compensation systems. The improved magnetometer prototype achieved a substantially enhanced sensitivity of 0.72±0.33 pT/√Hz, approaching the fundamental sensitivity limit of the system. Using atoms in the magnetic trap as a sensor, a sensitivity of 1.85 pT/√Hz was demonstrated. The system was verified to be photon-shot noise limited. Investigations into a double-pass probe configuration showed that, while the measured sensitivity was similar to that of the single-pass (4.3 pT/√Hz compared to 3.1 pT/√Hz at a probe power of 6.4 μW measured at the detector), the rotation angle increased by a factor of 2.2, with significantly reduced noise levels. These findings suggest that multi-pass strategies hold promise for enhanced performance in future implementations. In addition, the first signal detection from a BEC magnetometer, achieving 4.5 nT/√Hz with only 95,000 atoms at 35 nK was demonstrated.
Precision sensing, and in particular high precision magnetometry, is a central goal of research into quantum technologies. For magnetometers, often trade-offs exist between sensitivity, spatial resolution, and frequency range. The precision, and thus the sensitivity of magnetometry, scales as 1/sqrt[T_{2}] with the phase coherence time T_{2} of the sensing system playing the role of a key determinant. Adapting a dynamical decoupling scheme that allows for extending T_{2} by orders of magnitude and merging it with a magnetic sensing protocol, we achieve a measurement sensitivity even for high frequency fields close to the standard quantum limit. Using a single atomic ion as a sensor, we experimentally attain a sensitivity of 4.6 pT/sqrt[Hz] for an alternating-current magnetic field near 14 MHz. Based on the principle demonstrated here, this unprecedented sensitivity combined with spatial resolution in the nanometer range and tunability from direct current to the gigahertz range could be used for magnetic imaging in as of yet inaccessible parameter regimes.