Fig. 2: Representative correlation resonance spectrum of g⁽²⁾(0) and linewidth \({\cal{L}}\) behaviour.

a Exemplar of the weak measurement g⁽²⁾(0) resonance spectral profile with an HWHM of approximately 0.1 Hz, smaller than the coherence-lifetime-limited HWHM of ~1 Hz, obtained by setting D = 0.9995. As a comparison, the inset displays the corresponding spectrum without post-selection (D = 0). The “two-photon detuning” of the x-axis is equal to the Zeeman splitting of the ground states and is proportional to the total magnetic field, including the residual stray field inside the shield and the applied magnetic field to be measured. b Linear dependence of the full-width at half-maximum (FWHM) of the g⁽²⁾(0) resonance on the projection parameter D, for an input x-polarized cw laser of power 15 µW, which is in good agreement with the trend predicted by our theory.