Miniature biplanar coils for alkali-metal-vapor magnetometry

Atomic spin sensors offer precision measurements using compact, microfabricated packages, placing them in a competitive position for both market and research applications. Performance of these sensors such as dynamic range may be enhanced through magnetic field control. In this work, we discuss the design of miniature coils for three-dimensional, localized field control by direct placement around the sensor, as a flexible and compact alternative to global approaches used previously. Coils are designed on biplanar surfaces using a stream-function approach and then fabricated using standard printed-circuit techniques. Application to a laboratory-scale optically pumped magnetometer of sensitivity approximately 20 fT/Hz$^{1/2}$ is shown. We also demonstrate the performance of a coil set measuring $7 \times 17 \times 17$ mm$^3$ that is optimized specifically for magnetoencephalography, where multiple sensors are operated in proximity to one another. Characterization of the field profile using $^{87}$Rb free-induction spectroscopy and other techniques show $>$96% field homogeneity over the target volume of a MEMS vapor cell and a compact stray field contour of approximately 1% at 20 mm from the center of the cell.