We use Faraday spectroscopy of atoms confined to a crossed hollow beam trap to measure the magnetic field in a 200-micron-diameter spot with kilohertz sampling rate. Magnetic field maps are acquired by dynamic trap scanning.
Introduction The rapid development in recent decades of techniques for producing, trapping, and manipulating cold atoms has, as a side-benefit, made possible new methods of atomic magnetometry. The properties of cold atoms, including long coherence times and excellent spatial localization, are often desirable for high-precision magnetic sensing and allow the techniques of atomic magnetometry to be extended to previously inaccessible regions of parameter space. Specifically, the appeal of cold atoms for magnetometry lies in the demonstrated potential for high sensitivity at high spatial resolution. Magnetic-field measurements with atoms at finite temperature are generally characterized by motional averaging, in which atoms statistically sample a volume of space determined by the measurement time, the velocity distribution, and, if present, the confinement. For high-spatial-resolution magnetometry, atomic motion must be limited. The average displacement of atoms can be reduced by decreasing the measurement time, but a shorter measurement time is unappealing because it degrades the sensitivity of the measurement. Tighter confinement is an alternative means of reducing atomic motion, and is indeed attractive provided the confinement does not adversely affect the atomic spin coherence. The use of buffer gases in vapor-cell magnetometers is effectively a form of confinement, and indeed allows magnetometry with millimeter-scale spatial resolution. However, buffer gases are not entirely benign for atomic spins, having small but finite spin-destruction collisional cross-sections [1], whose effects would be increasingly deleterious at the high pressures necessary to achieve micrometer-scale resolution. A final alternative is to reduce the velocity spread by cooling the atomic ensemble; indeed, the use of cold atoms permits a significant reduction in motional averaging, and can be achieved with no loss (and potentially an increase) in spin-coherence time.
We demonstrate Faraday spectroscopy with a high duty cycle and sampling rate using atoms confined to a blue-detuned optical trap. Our trap consists of a crossed pair of high-charge-number hollow laser beams, which forms a dark, boxlike potential. We have used this to measure transient magnetic fields in a $500\text{\ensuremath{-}}\ensuremath{\mu}\text{m}$-diameter spot over a 400 ms time window with nearly unit duty cycle at a 500-Hz sampling rate. We use these measurements to quantify and compensate time-varying magnetic fields to $\ensuremath{\approx}10\text{ }$ nT per time sample.