In one embodiment, a method is provided. The method comprises: spin polarizing alkali atoms in a cavity; shifting resonant frequencies of the cavity at a rate proportional to a magnitude of a magnetic field incident upon the cavity; reflecting modulated right hand circularly polarized light and modulated left hand circularly polarized light from the cavity; transforming the reflected modulated right hand circularly polarized light to reflected modulated vertically polarized light, and the reflected modulated left hand circularly polarized light to reflected modulated horizontally polarized modulated light; generating a first error signal having an amplitude proportional to the shift in a resonant frequency corresponding to the reflected modulated vertically polarized light and a sign indicative of whether a frequency of the reflected modulated vertically polarized light is above or below the corresponding resonant frequency; generating a second error signal having an amplitude proportional to the shift in a resonant frequency corresponding to the reflected modulated horizontally polarized light and a sign indicative of whether a frequency of the reflected modulated horizontally polarized light is above or below the corresponding resonant frequency; adjusting a carrier frequency of the modulated right hand circularly polarized light in response to the first error signal; adjusting a carrier frequency of the modulated left hand circularly polarized light in response to the second error signal; and generating a measured Larmor frequency.