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We describe a finite fields magnetic gradiometer using an intense pulsedlaser to polarize a $^{87}$Rb atomic ensemble and a compact VCSEL probe laserto detect paramagnetic Faraday rotation in a single multipass cell. We reportdifferential magnetic sensitivity of $14$ fT/Hz$^{1/2}$ over a broad dynamicrange including Earth's field magnitude and common-mode rejection ratio higherthan $10^4$. We also observe a nearly quantum-noise-limited behaviour of thegradiometer, by comparing the experimental standard deviation of the estimatedfrequency difference against the Cram\'{e}r-Rao lower bound in the presence ofwhite photon shot-noise, atomic spin noise and atomic diffusion.

Femtotesla nearly quantum-noise-limited pulsed gradiometer at Earth-scale fields