  We describe a novel pulsed magnetic gradiometer based on the optical
interference of sidebands generated using two spatially separated alkali vapor
cells. The sidebands are produced with high efficiency using parametric
frequency conversion of a probe beam interacting with $^{87}$Rb atoms in a
coherent superposition of magnetically sensitive hyperfine ground states.
Interference between the sidebands generates a low-frequency beat note whose
frequency is determined by the magnetic field gradient between the two vapor
cells. In contrast to traditional magnetic gradiometers, our approach provides
a direct readout of the gradient field without the intermediate step of
subtracting the outputs of two spacially separated magnetometers. The technique
is expected to provide effective common-mode magnetic field cancellation at
frequencies far greater than the bandwidth of the gradiometer. Using this
technique, we developed a compact magnetic gradiometer sensor head with
integrated optics with a sensitivity of $25 \ fT/cm/\sqrt{Hz}$ with a $4.4$ cm
baseline, while operating in a noisy laboratory environment unshielded from
Earth's field. We also outline a theoretical framework that accurately models
sideband generation using a density matrix formalism.
