Absorptive laser threshold magnetometry: Combining visible diamond Raman lasers and nitrogen-vacancy centres

We propose a high-sensitivity magnetometry scheme based on a diamond Raman laser with visible pump absorption by an ensemble of coherently microwave driven negatively charged nitrogen-vacancy centres (NV−) in the same diamond crystal. The NV− centres' absorption and emission are spin-dependent. We show how the varying absorption of the NV− centres changes the Raman laser output. A shift in the diamond Raman laser threshold and output occurs with the external magnetic field and microwave driving. We develop a theoretical framework with steady-state solutions to describe the effects of coherently driven NV− centres including the charge state switching between NV− and its neutral charge state NV0 in a diamond Raman laser. We discuss that such a laser working at the threshold can be employed for magnetic field sensing. In contrast to previous studies on NV− magnetometry with visible laser absorption, the laser threshold magnetometry method is expected to have low technical noise, due to low background light in the measurement signal. For magnetic-field sensing, we project a shot-noise limited DC sensitivity of a few pT $/\sqrt{\mathrm{H}\mathrm{z}}$ in a well-calibrated cavity with realistic parameters. This sensor employs the broad visible absorption of NV− centres and unlike previous laser threshold magnetometry proposals it does not rely on active NV− centre lasing or an infrared laser medium at the specific wavelength of the NV− centre's infrared absorption line.