Parity-time-symmetry-breaking gyroscopes: lasing without gain and subthreshold regimes

We show that the lasing threshold for two coupled resonators (CRs) corresponds to lasing without gain (LWG), a phenomenon analogous to lasing without inversion in atomic systems, when parity-time (PT) symmetry is broken. The use of LWG for gyroscopes may resolve some of the difficulties associated with PT-symmetric gyroscopes. In particular, we find that PT-symmetric systems suffer from undamped Rabi oscillations, whereas LWG systems are overdamped. In addition, observation of enhanced sensitivity should be more straightforward in LWG gyros because the enhancement remains above unity even at couplings far from the exceptional point (EP). Finally, LWG gyros operate more like conventional laser gyroscopes with one frequency for each output direction, and therefore there is no ambiguity in the direction of rotation. Gain saturation in CR systems is found to dramatically boost the size of the sensitivity enhancement, eliminate the Rabi oscillations, and enlarge the parameter space around the EP over which the enhancement is expected to occur. A second situation with broken symmetry is also examined: CR systems below threshold. Whereas the pole in sensitivity coincides with the EP at threshold, the pole can occur far away from the EP for subthreshold systems. Our analysis also puts previous results on passive and active fast-light cavities using atomic vapor cells into the context of EP-enhanced sensing with non-Hermitian Hamiltonians.