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Atom interferometers provide exquisite measurements of the properties ofnon-inertial frames. While atomic interactions are typically detrimental togood sensing, efforts to harness entanglement to improve sensitivity remaintantalizing. Here we explore the role of interactions in an analogy betweenatomic gyroscopes and SQUIDs, motivated by recent experiments realizing ringshaped traps for ultracold atoms. We explore the one-dimensional limit of thesering systems with a moving weak barrier, such as that provided by ablue-detuned laser beam. In this limit, we employ Luttinger liquid theory andfind an analogy with the superconducting phase-slip qubit, in which thetopological charge associated with persistent currents can be put intosuperposition. In particular, we find that strongly-interacting atoms in such asystem could be used for precision rotation sensing. We compare the performanceof this new sensor to an equivalent non-interacting atom interferometer, andfind improvements in sensitivity and bandwidth beyond the atomic shot-noiselimit.

Interacting atomic interferometry for rotation sensing approaching the Heisenberg Limit