  Higher-order exceptional points in non-Hermitian systems have recently been
used as a tool to engineer high-sensitivity devices, attracting tremendous
attention from multidisciplinary fields. Here, we present a simple yet
effective scheme to enhance the device sensitivity by slightly deviating the
gain-neutral-loss linear configuration to a triangular one, resulting in an
abrupt phase transition from third-order to second-order exceptional points.
Our analysis demonstrates that the exceptional points can be tailored by a
judicious tuning of the coupling parameters of the system, resulting in
enhanced sensitivity to a small perturbation. The tunable coupling also leads
to a sharp change in the sensitivity slope, enabling the perturbation to be
measured precisely as a function of coupling. This two-way detection of the
perturbation opens up a rich landscape toward ultra-sensitive measurements,
which could be applicable to a wide range of non-Hermitian ternary platforms.
