Fig. 4: MW cavity readout magnetometer sensitivity.

Based on noise spectral density measured during magnetometer operation (blue solid line), we project a sensitivity of ≈ 3 \(\,\text{pT}/\sqrt{\text{Hz}\,}\) in the band from 5 kHz to 10 kHz, where sensitivity approaches the limit set by the measured noise floor of the amplifier and digitizer electronics (red solid line). Also depicted are the optical-readout shot-noise limit (black short dashed line) of the experimental setup, the calculated Johnson-Nyquist noise limit (black long dashed line) of 0.5 \(\,\text{pT}/\sqrt{\text{Hz}\,}\) and the optical-pumping-limited spin-projection limit (black dotted line). The optical-pumping-limited spin-projection limit is bounded above and below (gray shaded box) to illustrate uncertainty arising from estimating the optical pumping relaxation time \({T}_{1}^{\,\text{op}\,}\) (see Methods). Magnetometry is performed using the phase-sensitive technique of recording reflected MW voltage through the IQ mixer; IQ traces are shown in Supplementary Note 5.