Intrinsic Pulsed Magnetic Gradiometer in Earth's Field

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.