Properties Of non-Hermitian Systems Research Articles

Kibble−Zurek scaling of the dynamical localization−skin effect phase transition in a non-Hermitian quasi-periodic system under the open boundary condition

In the present study, the driven dynamics in a non-Hermitian Aubry–André (AA) model under the open boundary condition (OBC) are studied. For this model, non-Hermiticity is introduced by the non-reciprocal hopping, and this model undergoes a localization–skin effect phase transition depending on the strength of the quasi-periodic potential. Although the properties of non-Hermitian systems are very sensitive to the imposed boundary conditions, we find that the scaling behavior can also be described by the same set of the exponents under the periodic boundary condition (PBC). When the initial state is prepared deep in the localized phase and the potential strength is slowly driven through the critical point, we find that the driven dynamics of the localization length ξ and the inverse participation ratio (IPR) could be described by the Kibble–Zurek scaling (KZS). Then, we numerically verify these predictions for different initial states. Finally, the dynamical emergence of the skin effect state is found, and the dynamics can also be described by the Kibble−Zurek scaling with the same set of critical exponents.

Non-Hermitian mosaic dimerized lattices

Non-Hermitian systems have attracted much attention during the past few years, both theoretically and experimentally. The existence of non-Hermiticity can induce multiple exotic phenomena that cannot be observed in Hermitian systems. In this work, we introduce a new non-Hermitian system called the non-Hermitian mosaic dimerized lattice. Unlike the regular nonreciprocal lattices where asymmetric hoppings are imposed on every hopping term, here in the mosaic dimerized lattices the staggered asymmetric hoppings are only added to the nearest-neighboring hopping terms with equally spaced sites. By investigating the energy spectra, the non-Hermitian skin effect (NHSE), and the topological phases in such lattice models, we find that the period of the mosaic asymmetric hopping can influence the system’s properties significantly. For a system with real system parameters, we find that as the strength of asymmetric hopping increases, the energy spectra of the system under open boundary conditions will undergo a real-imaginary or real-complex transition. As to the NHSE, we find that when the period is odd, there appears no NHSE in the system and the spectra under open boundary conditions (OBCs) and periodic boundary conditions (PBCs) are the same (except for the topological edge modes under OBCs). If the period of the mosaic asymmetric hopping is even, the NHSE will emerge and the spectra under different boundary conditions exhibit distinctive structures. The PBC spectra form loop structures, indicating the existence of point gaps that are absent in the spectra under OBCs. The point gap in the PBC spectrum is shown to be the topological origin of the NHSE under OBCs, which also explains the NHSE in our mosaic dimerized lattices. To distinguish whether the bulk states of the system under OBCs are shifted to the left or right end of the one-dimensional lattice due to the NHSE, we define a new variable called the directional inverse participation ratio (dIPR). The positive dIPR indicates that the state is localized at the right end while the negative dIPR corresponds to the states localized at the left end of the one-dimensional lattice. We further study the topological zero-energy edge modes and characterize them by calculating the Berry phases based on the generalized Bloch Hamiltonian method. In addition, we also find that the topological edge modes with nonzero but constant energy can exist in the system. Our work provides a new non-Hermitian lattice model and unveils the exotic effect of mosaic asymmetric hopping on the properties of non-Hermitian systems.

Arbitrary order exceptional point induced by photonic spin\u2013orbit interaction in coupled resonators

Many novel properties of non-Hermitian systems are found at or near the exceptional points—branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. In particular, higher-order exceptional points can result in optical structures that are ultrasensitive to external perturbations. Here we show that an arbitrary order exceptional point can be achieved in a simple system consisting of identical resonators placed near a waveguide. Unidirectional coupling between any two chiral dipolar states of the resonators mediated by the waveguide mode leads to the exceptional point, which is protected by the transverse spin–momentum locking of the guided wave and is independent of the positions of the resonators. Various analytic response functions of the resonators at the exceptional points are experimentally manifested in the microwave regime. The enhancement of sensitivity to external perturbations near the exceptional point is also numerically and analytically demonstrated.

Detecting topological exceptional points in a parity-time symmetric system with cold atoms.

We reveal a novel topological property of the exceptional points in a two-level parity-time symmetric system and then propose a scheme to detect the topological exceptional points in the system, which is embedded in a larger Hilbert space constructed by a four-level cold atomic system. We show that a tunable parameter in the presented system for simulating the non-Hermitian Hamiltonian can be tuned to sweep the eigenstates through the exceptional points in parameter space. The non-trivial Berry phases of the eigenstates obtained in this loop from the exceptional points can be measured by the atomic interferometry. Since the proposed operations and detection are experimentally feasible, our scheme may pave a promising way to explore the novel properties of non-Hermitian systems.