Boosting the Rotational Sensitivity of Matter-wave Interferometry with Nonlinearity

We propose a mechanism to use nonlinearity arising from inter-particle interactions to significantly enhance rotation sensitivity of matter-wave interferometers. The method relies on modifying Sagnac interferometers by introducing a weak circular lattice potential that couples modes with opposite orbital angular momenta (OAM). The primary observable comprises of the modal population distributions measured at particular times. This provides an alternate mechanism for rotation sensing that requires substantially smaller ring size, even in the linear non-interacting regime. Nonlinearity can improve the sensitivity, as well as operation timescales, by several orders of magnitude.