Non-adiabatic Non-Hermitian Sensing enabled by Criticality-Enhanced Topological Tunneling

Non-Hermitian sensing is an intriguing mechanism that utilizes the nonlinear responses near the exceptional points (EPs) to amplify external perturbations with unprecedented precision. While promising transformative sensitivity, existing approaches face stringent limitations due to their reliance on quasi-static state responses and simultaneously encountering divergent noise arising from eigenstate collapse. Here, we propose a non-adiabatic sensing paradigm leveraging parameter-sensitive non-Hermitian tunneling, which surmounts the limitations of adiabatic approaches. This sensitivity, under a metric transformation, is governed by the phase change rate-modulated by the external signal-with geometric amplification, manifesting (i) criticality enhancement (quantum metric divergence near EPs) and (ii) chiral selectivity governed by path- and state-dependent imaginary intraband Berry connections. Experimentally, we validate this paradigm through direct measurements of the Fisher information on a trapped-ion platform. This work establishes a pathway to practical non-Hermitian sensing with non-Abelian non-adiabatic processes.