Ring Bose-Einstein condensate in a cavity: Chirality detection and rotation sensing

Recently, a method has been proposed to detect the rotation of a ring Bose-Einstein condensate, in situ, in real-time, and with minimal destruction by using a cavity driven with optical fields carrying orbital angular momentum [Phys. Rev. Lett. 127, 113601 (2021)]. This method is sensitive to the magnitude of the condensate winding number but not its sign. In the present work, we consider simulations of the rotation of the angular lattice formed by the optical fields and show that the resulting cavity transmission spectra are sensitive to the sign of the condensate winding number. We demonstrate the minimally destructive technique on persistent current rotational eigenstates, counter-rotating superpositions, and a soliton singly or in collision with a second soliton. Conversely, we also investigate the sensitivity of the ring condensate, given knowledge of its winding number, to the rotation of the optical lattice. This characterizes the effectiveness of the optomechanical configuration as a laboratory rotation sensor. Our results are important to studies of rotating ring condensates used in atomtronics, superfluid hydrodynamics, simulation of topological defects and cosmological theories, interferometry using matter-wave solitons, and optomechanical sensing.