Reconstruction-free quantum sensing of arbitrary waveforms

We present a protocol for directly detecting time-dependent magnetic field waveforms with a quantum two-level system. Our method is based on a differential refocusing of segments of the waveform using spin echoes. The sequence can be repeated to increase the sensitivity to small signals. The frequency bandwidth is intrinsically limited by the duration of the refocusing pulses. We demonstrate detection of arbitrary waveforms with $\sim 20 {\rm ns}$ time resolution and $\sim 4\mu{\rm T}/\sqrt{\rm Hz}$ field sensitivity using the electronic spin of a single nitrogen-vacancy center in diamond.