Detection of a weak magnetic field via cavity enhanced Faraday rotation

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We study the sensitive detection of a weak static magnetic field via Faraday rotation induced by an ensemble of spins in a bimodal degenerate microwave cavity. We determine the limit of the resolution for the sensitivity of the magnetometry achieved using either single-photon or multiphoton inputs. For the case of a microwave cavity containing an ensemble of Nitrogen-vacancy defects in diamond, we obtain a magnetometry sensitivity exceeding 0.5 /√, utilizing a single photon probe field, while for a multiphoton input we achieve a sensitivity about 1 /√, using a coherent probe microwave field with power of Pᵢn=1.