Observing non-Bloch braids and phase transitions by precise manipulation of the non-Hermitian boundary and size

The complex spectrum of non-Hermitian topological systems manifests extreme sensitivity to boundary perturbations when the system size is large. Hence, despite precise manipulation of non-Hermitian boundaries and sizes remains a challenge, it is of fundamental importance in developing ultra-sensitive sensing devices. Here, we address this issue using a non-Hermitian static mechanical lattice platform, with the lower bound of the accessible boundary perturbation being 10−22, about tens of orders of magnitude better than current systems, for a maximal size exceeding 102. This performance facilitates the exploration of various extreme non-Hermitian phenomena. As a proof of concept, we demonstrate theoretically the braid topology of non-Hermitian non-Bloch bands, whose sensitivity increases exponentially with the size. Based on the static platform, we measure experimentally ultra-sensitive braid phase transitions. Our study unveils the nontrivial interplay among non-Hermiticity, braid topology, and spectral sensitivity, and reaches a much improved level of controllable non-Hermitian boundaries and sizes. The spectrum of non-Hermitian Hamiltonians is highly sensitive to boundary perturbations. Here, the authors show how this ultrasensitivity can be manipulated in static mechanical platforms by demonstrating a phase transition of non-Bloch eigenvalue braids with ultra-high precision, triggered by local boundary perturbations or system sizes.