One-dimensional rings with barriers: a Luttinger liquid approach to precision measurement

Recent experiments [1] have realized ring shaped traps for ultracold atoms in which the atoms can be manipulated in several interesting ways. Here, we consider 1D ring system with a moving weak barrier within the framework of Luttinger liquid theory. We find that classical theory suggests high precision sensors can be constructed from these systems; we extend these results into the quantum regime. \\[4pt] [1] Wright, K., et al. Driving phase slips in a superfluid atom circuit with a rotating weak link. Phys. Rev. Lett. 110, 025302~(2013)