An array of 21 first-order gradiometers based on zero-field optically-pumped magnetometers is demonstrated for use in magnetoencephalography. Sensors are oriented radially with respect to the head and housed in a helmet with moveable holders which conform to the shape of a scalp. Our axial gradiometers have a baseline of 2 cm and reject laser and vibrational noise as well as common-mode environmental magnetic noise. The median sensitivity of the array is 15.4 fT/Hz1/2, measured in a human-sized magnetic shield. All magnetometers are operated independently with negative feedback to maintain atoms at zero magnetic field. This yields higher signal linearity and operating range than open-loop operation and a measurement system that is less sensitive to systematic and ambient magnetic fields. All of the system electronics and lasers are compacted into one equipment rack which offers a favorable outlook for use in clinical settings.

Magnetoencephalography (MEG) measures small magnetic fields (femtotesla to picotesla) generated by neuronal currents within the brain and has led to insights into neural activity at millisecond time scales (Supek and Aine 2014). Most MEG systems are based on low-temperature superconducting quantum interference devices (SQUIDs). The SQUIDs are housed in a helmet-shaped liquid helium dewar with roughly 2 cm of space between the SQUIDs and the inside surface of the helmet. Since the magnetic field falls off quickly with distance from the source, e.g. 1/r 3 for magnetic dipoles, the distance between the sensors and scalp is important for the quality of the MEG images. This problem is compounded by the fixed positions of the low-temperature SQUIDs cannot account for differences in a patient's head shape and size. On-scalp sensors, such as optically-pumped magnetometers (OPMs) and arrays of high-temperature SQUIDs (Zhang et al 1993, Dammers et al 2014, Pfeiffer et al 2019), can be arranged in geometries conformal to the head, independent of the size and shape. Recent studies simulating whole-head MEG systems with on-scalp sensors promise greatly increased spatial resolution compared to the current SQUID-based MEG systems (Luessi et al 2014, Boto et al 2016, Iivanainen et al 2017).In the OPMs used here, 87 Rb atoms are confined in a microfabricated vapor cell (Liew et al 2004) made from silicon and glass. Light at 795 nm, on resonance with the D1 transition in 87 Rb, is circularly polarized and used to create a spin-polarization in the 87 Rb atoms. The transmitted light power is altered as a function of the magnetic field at the location of the vapor cell. A detailed description of the sensor geometry can be found in Sheng et al (2017). In order to reach high field sensitivities, the OPMs are operated in the regime where decoherence from spin-exchange collisions is suppressed: at very low ambient magnetic fields and high 87 Rb densities (Happer and Tang 1973, Allred et al 2002). Nitrogen at a density of roughly 1 amagat is used as a buffer gas to inhibit 87 Rb collisions with the cell walls as well as a quenching gas to limit radiation trapping, both of which are necessary to increase the spin-coherence time at high density. The zero-field resonance is measured by monitoring the transmission of light from a single laser beam through the vapor cell (Dupont-Roc et al 1969). This creates a symmetric resonance lineshape centered around zero magnetic field. A small magnetic modulation field of a few kilohertz and about 100 nanotesla is applied in a direction perpendicular to the laser beam. Phase-sensitive detection of the transmission signal at this modulation frequency yields a dispersive resonance as the magnetic

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Comparisons of high-accuracy optical atomic clocks [1] are essential for precision tests of fundamental physics [2], relativistic geodesy [3][4][5], and the anticipated redefinition of the SI second [6]. The scientific reach of these applications is restricted by the statistical precision of interspecies comparison measurements. The instability of individual clocks is limited by the finite coherence time of the optical local oscillator (OLO), which bounds the maximum atomic interrogation time. In this letter, we experimentally demonstrate differential spectroscopy [7], a comparison protocol that enables interrogating beyond the OLO coherence time. By phase-coherently linking a zero-dead-time (ZDT) [8] Yb optical lattice clock with an Al + single-ion clock via an optical frequency comb and performing synchronised Ramsey spectroscopy, we show an improvement in comparison instability relative to our previous result [9] of nearly an order of magnitude. To our knowledge, this result represents the most stable interspecies clock comparison to date. II. MAIN