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Developing robust microwave-field sensors is both fundamentally andpractically important with a wide range of applications from astronomy tocommunication engineering. The Nitrogen-Vacancy (NV) center in diamond is anattractive candidate for such purpose because of its magnetometric sensitivity,stability and compatibility with ambient conditions. However, the existing NVcenter-based magnetometers have limited sensitivity in the microwave band. Herewe present a continuous heterodyne detection method that can enhance thesensor's response to weak microwaves, even in the absence of spin controls.Experimentally, we achieve a sensitivity of 8.9 pT$\cdot$Hz$^{-1/2}$ formicrowaves of 2.9 GHz by simultaneously using an ensemble of $n_{\text{NV}}\sim 2.8\times10^{13}$ NV centers within a sensor volume of $4\times10^{-2}$mm$^3$. Besides, we also achieve $1/t$ scaling of frequency resolution up tomeasurement time $t$ of 10000 s. Our method removes the control pulses and thuswill greatly benefit the practical application of diamond-based microwavesensors.

Picotesla magnetometry of microwave fields with diamond sensors