Gradient Field Detection Using Interference of Stimulated Microwave Optical Sidebands

We demonstrate that stimulated microwave optical sideband generation using parametric frequency conversion can be utilized as a powerful technique for coherent state detection in atomic physics experiments. The technique has advantages over traditional absorption or polarization rotation-based measurements and enables the isolation of signal photons from probe photons. We outline a theoretical framework that accurately models sideband generation using a density matrix formalism. Using this technique, we demonstrate a novel intrinsic magnetic gradiometer that detects magnetic gradient fields between two spatially separated vapor cells by measuring the frequency of the beat note between sidebands generated within each cell. 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 gradiometers the intermediate step of measuring the magnetic field experienced by the two vapor cells is unnecessary. We show that this technique can be readily implemented in a practical device by demonstrating a compact magnetic gradiometer sensor head 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.