Efficient evolution framework for chirality control in non-Hermitian systems with adiabaticity engineering

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. Here, we introduce a method which dynamically engineers the adiabaticity in the evolution of non-Hermitian Hamiltonians that allows for both chiral and nonchiral mode conversion on the same path. Our method is based on quantifying and controlling the instantaneous adiabaticity, allowing for nonuniform evolution throughout the entire path. We apply our method into the microwave waveguide system and by optimizing the distributed adiabaticity along the evolution loop, we achieve the same quality of mode conversion as conventional quasiadiabatic evolution in only one-fourth of the time. Our approach provides an on-demand solution to address the speed and chirality challenges associated with EP encircling, which does not depend on specific model. It also facilitates the dynamic manipulation and regulation of nonadiabatic processes, thereby accelerating the operation and allowing for a selection among various mode conversion patterns.