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In the last few years, the great utility of exceptional points in sensing linear perturbations has been recognized. However, physical systems are inherently anharmonic and macroscopic physics is most accurately described by nonlinear models. Considering the multitude of semiclassical and quantum effects ensuing from nonlinear interactions, the sensing of anharmonicities is a prerequisite to the primed control of these effects. Here, we propose an expedient sensing scheme relevant to dissipatively coupled anti parity-time (anti-PT) symmetric systems and customized for the fine-grained estimation of anharmonic perturbations. The sensitivity to anharmonicities is derived from the coherence between two modes induced by a common vacuum. Owing to this coherence, the linear response acquires a pole on the real axis. We demonstrate how this singularity can be exploited for the enhanced sensing of very weak …