Exploring nonreciprocal noise transfer under Onsager-Casimir symmetry in synthetic-field optomechanics

An optomechanical system of fundamental importance consists of two intercoupled mechanical resonators, which are radiation-pressure coupled individually to a photonic cavity. This closed-loop and overall lossy configuration possesses two exceptional points (EPs) and offers the realization of synthetic magnetism, controlled by the loop phase. To elucidate the intricate role of loop phase and EPs in this setting, we analyze the noise power spectral density profiles of internal as well as output fluctuations. In the presence of a synthetic magnetic field, the nonreciprocal routing of a signal is well known. Here, we further show that this also applies to nonreciprocal backaction noise flow when the time-reversal symmetry is broken, while the Onsager-Casimir symmetry still holds. To better quantify this phenomenon, we introduce a nonreciprocity measure that contrasts the time-reversed counterparts as a function of loop phase. We observe that nonreciprocal noise flow is enhanced for smaller intermechanical couplings at the expense of lower sensitivity, whereas for sensing purposes, using a higher intermechanical coupling constant is the more viable option.