Millihertz magnetic resonance spectroscopy combining the heterodyne readout based on solid-spin sensors

The sensitivities of quantum sensing in metrology and spectroscopy are drastically influenced by the resolution of the frequency spectrum. However, the resolution is hindered by the decoherence effect between the sensor and the environment. Along these lines, the continue-wave optically detected magnetic resonance (CWODMR) method combined with the heterodyne readout was proposed to break the limitation of the sensor's coherence time. The frequency of the magnetic field was swept to match the unknown signal, and the signal can be transformed to a real-time frequency-domain curve via the heterodyne readout, with a frequency resolution of 4.7 millihertz. Using the nitrogen-vacancy (NV) center ensemble in a diamond as the solid-spin sensors, it was demonstrated that the frequency resolution and precision could be improved proportionally to the low-pass filter parameters of T_c ^-1 and T_c ^-1.5, respectively. Furthermore, the introduced method performed the sensing of arbitrary audio signals with a sensitivity of 7.32 nT·Hz^-1/2@10 kHz. Our generic approach can be extended to several fields, such as molecular structure determination and biomagnetic field detection, where high-fidelity detection properties across multiple frequency bands are required within small sensing volumes (∼ mm³).