Dynamical topology of chiral and nonreciprocal state transfers in a non-Hermitian quantum system

Topological phenomena are fundamentally underlain by the geometric phase of eigenstates. Time-varying Hamiltonians furthermore allow for a dynamical topological invariant associated with continuous flows. We study chiral and nonreciprocal dynamics by encircling the exceptional points (EPs) of non-Hermitian Hamiltonians in a trapped ion system. We find that these dynamics are topologically robust against external perturbations even in the presence of dissipation-induced nonadiabatic transitions. Furthermore, our results indicate that these behaviors are protected by dynamical vorticity—an emerging topological invariant associated with the energy dispersion of non-Hermitian band structures in a parallel transported eigenbasis. Through the quantum state tomography, the symmetry breaking and other key features of topological dynamics are directly verified. These results mark a significant step towards exploring topological properties of open quantum systems. The complex energy surface of a non-Hermitian system is not single-valued, and windings around its so-called exceptional branching points lead to the chiral and non-reciprocal transfer of eigenstates. Here, the authors experimentally demonstrate such topological state transfers in trapped ion systems, which are being established as promising platforms for quantum simulation.