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The eigenvalue of a non-Hermitian Hamiltonian often forms a self-intersecting Riemann surface, leading to a unique mode conversion phenomenon when the Hamiltonian evolves along certain loop paths around an exceptional point (EP). However, two fundamental problems exist with the conventional scheme of EP encircling: the speed of mode conversion is restricted by the adiabatic requirement, and the chirality cannot be freely controlled. We introduce a method for dynamically engineering adiabaticity in the evolution of non-Hermitian Hamiltonians that allows for both chiral and non-chiral mode conversion on the same path. Our method is based on quantifying and controlling the instantaneous adiabaticity, allowing for non-uniform evolution throughout the entire path. By optimizing the evolution based on the distributed nature of adiabaticity, we achieve the same quality as conventional quasi-adiabatic evolution in only one-third of the time. Our approach provides a comprehensive and universal solution to address the speed and chirality challenges associated with EP encircling. It also facilitates the dynamic manipulation and regulation of non-adiabatic processes, thereby accelerating the operation and allowing for a selection among various mode conversion patterns.

Time reversal (T) invariant topological insulator is widely recognized as one of the fundamental discoveries in condensed matter physics, for which the most fascinating hallmark is perhaps a spin based topological protection, the total cancellation of scattering of conduction electrons with certain spins on matter surface. Recently, it has created a paradigm shift for topological insulators, from electronics to photonics, phononics as well as mechanics, bringing about not only involved new physics but also potential applications in robust wave transport. Despite the growing interests in realizing topologically protected acoustic wave transport, T-invariant acoustic topological insulator has not yet been achieved. Here, we report the first demonstration of acoustic topological insulator: a strongly coupled metamaterial ring lattice that supports one-way propagation of helical edge states under T-symmetry, backscattering immune to boundary abrupt variations. The very unique thing is the formation of spin-filtered interface states due to lattice dislocations. The mechanism underlying the formation of topologically protected edge states and interface states is applicable in various other wave systems or higher dimensions., Comment: 20 pages, 4 figures