Sub-millihertz magnetic spectroscopy with a nanoscale quantum sensor

Precise timekeeping is critical to metrology, forming the basis by which standards of time, length and fundamental constants are determined. Stable clocks are particularly valuable in spectroscopy as they define the ultimate frequency precision that can be reached. In quantum metrology, where the phase of a qubit is used to detect external fields, the clock stability is defined by the qubit coherence time, which determines the spectral linewidth and frequency precision. Here we demonstrate a quantum sensing protocol where the spectral precision goes beyond the sensor coherence time and is limited by the stability of a classical clock. Using this technique, we observe a precision in frequency estimation scaling in time $T$, as $T^{-3/2}$ for classical oscillating fields. The narrow linewidth magnetometer based on single spins in diamond is used to sense nanoscale magnetic fields with an intrinsic frequency resolution of 607 $\mu$Hz, 8 orders of magnitude narrower than the qubit coherence time.