Quantum enhanced SU(1,1) matter wave interferometry in a ring cavity

Quantum squeezed states offer metrological enhancement as compared to their classical counterparts. Here, we devise and numerically explore a novel method for performing SU(1,1) interferometry beyond the standard quantum limit, using quasi-cyclic nonlinear wave mixing dynamics of ultracold atoms in a ring cavity. The method is based on generating quantum correlations between many atoms via photon mediated optomechanical interaction. Timescales of the interferometer operation are here given by the inverse of photonic recoil frequency, and are orders of magnitude shorter than the timescales of collisional spin-mixing based interferometers. Such shorter timescales should enable not only faster measurement cycles, but also lower atomic losses from the trap during measurement, which may lead to significant quantum metrological gain of matter wave interferometry in state of the art cavity setups.