Anti-PT-Symmetric Optical Gyroscope at the Transmission Peak Degeneracy With Enhanced Signal-to-Noise Ratio

Non-Hermitian sensors have been widely studied for the enhanced response of their eigenvalues in the proximity of exceptional points. However, it has been shown that noise is enhanced in the same way as sensitivity, thus vanishing the advantages of the exceptional point. Recently, the idea of measuring the frequency splitting of transmission peaks of a non-lasing PT-symmetric sensor has shown the possibility of increasing the signal-to-noise ratio of a sensor close to the so called 'transmission peak degeneracy', with respect to an operating condition away from it. Here we analyze a non-Hermitian optical gyroscope, demonstrating that also anti-PT-symmetric Hamiltonians show an enhanced transmission peaks frequency splitting in the proximity of the transmission peak degeneracy. We also perform an analysis on noise and uncertainties and introduce new figures of merit to compare the proposed anti-PT-symmetric sensor with a classical resonant optical gyroscope. When the uncertainties due to fluctuations of parameters are negligible with respect to the uncertainties due to amplitude noise, the non-Hermitian sensor working at the transmission peak degeneracy is demonstrated to operate better than a classical resonant gyroscope in terms of signal-to-noise ratio.