PT-Symmetric Topological Edge-Gain Effect

Anomalous Non-Hermitian Open-Boundary Spectrum

For a long time, it was presumed that continuum bands could be readily encompassed by open-boundary spectra, irrespective of the system's modest dimensions. However, our findings reveal a nuanced picture: under open-boundary conditions, the proliferation of complex eigenvalues progresses in a sluggish, oscillating manner as the system expands. Consequently, even in larger systems, the overlap between continuum bands and open-boundary eigenvalues becomes elusive, with the surprising twist that the count of these complex eigenvalues may actually diminish with increasing system size. This counterintuitive trend underscores that the pursuit of an ideal, infinite-sized system scenario does not necessarily align with enlarging the system size. Notably, despite the inherent non-Hermiticity of our system, the eigenstates distribute themselves in a manner reminiscent of Bloch waves. These discoveries hold potential significance for both theoretical explorations and experimental realizations of non-Hermitian systems.

Mode-order conversion in a Mach-Zehnder interferometer based on Chern insulators

Mode-order conversion devices can provide a flexible platform to achieve mode coupling and optimizing in mode division multiplex (MDM) that can eliminate the restrain of capacity and density in photonic integration and communication. However, mode-order converters based on traditional photonic crystal (PC) waveguides are susceptible to defects, which always render device incapacitation in mode-order conversion. Herein, a mode converter designed by the Mach-Zehnder interferometer (MZI) structure is proposed to manipulate the conversion of topological edge states (TESs) based on Chern insulators consisting of gyromagnetic PCs. The back-and-forth conversion between fundamental and high-order modes is numerically demonstrated based on phase modulation in our proposed device, in which each mode can be immune to defects. This unique approach for converting the mode order of TES exploits a new perspective in MDM to design a high-performance multimode device, leading to potential applications in photonic integrated circuits (PIC), on-chip processors, and optical fiber communication.

Advances and applications on non-Hermitian topological photonics

Non-Hermitian photonics and topological photonics, as new research fields in optics, have attracted much attention in recent years, accompanying by a great deal of new physical concepts and novel effects emerging. The two fields are gradually crossed during the development process and the non-Hermitian topological photonics was born. Non-Hermitian topological photonics not only constantly produces various novel physical effects, but also shows great potential in optical device applications. It becomes an important part of the modern physics and optics, penetrating into different research fields. On one hand, photonics system can introduce artificially-constructed gain and loss to study non-Hermitian physics. Photonics platform is an important methods and ways to verify novel physical phenomena and promote the development of non-Hermitian physics. On the other hand, the non-Hermitian topological photonics provides a new dimension for manipulating topological states. Active and dissipate materials are common in photonic systems; therefore, by using light pump and dissipation of photonic systems, it is expected to promote further development of topological photonics in device applications. In this review article, we focus on the recent advances and applications on non-Hermitian topological photonics, including the non-Hermitian topological phase transition and skin effect, as well as the applications emerging prosperously in reconfigurable, nonlinear and quantum optical systems. The possible future research directions of non-Hermitian topological photonics are also discussed at the end. Non-Hermitian topological photonics can have great potential in technological revolution and have the capacity of leading the development of both physics and technology industry.

Topological optical parametric oscillation

Topological insulators possess protected boundary states which are robust against disorders and have immense implications in both fermionic and bosonic systems. Harnessing these topological effects in nonequilibrium scenarios is highly desirable and has led to the development of topological lasers. The topologically protected boundary states usually lie within the bulk bandgap, and selectively exciting them without inducing instability in the bulk modes of bosonic systems is challenging. Here, we consider topological parametrically driven nonlinear resonator arrays that possess complex eigenvalues only in the edge modes in spite of the uniform pumping. We show parametric oscillation occurs in the topological boundary modes of one and two dimensional systems as well as in the corner modes of a higher order topological insulator system. Furthermore, we demonstrate squeezing dynamics below the oscillation threshold, where the quantum properties of the topological edge modes are robust against certain disorders. Our work sheds light on the dynamics of weakly nonlinear topological systems driven out-of-equilibrium and reveals their intriguing behavior in the quantum regime.

Topological boundary states of two-dimensional restricted isosceles triangular photonic crystals

We propose an all-media photonic crystal (PC) composed of isosceles triangle dielectric cylinders that realizes the topological phase transition by simply rotating the isosceles triangular dielectric cylinders. Additionally, the topological phase transition is closely linked with the size parameters and rotation angle of the isosceles triangle. The topological boundary states with lossless transmission are constructed on the interface of two different topological structures, and the optical quantum spin Hall effect is simulated. Further, we verified that the boundary state is unidirectional and immune to disorder, cavity, and sharp bend defects. By rotating the angle of the triangle to control the transmission path of the pseudo-spin state, we realize diverse transport pathways of light, such as the "straight line" shape, "Z" shape, "U" shape, and "Y" shape. This topological system shows a higher degree of freedom, which can promote the research on topological boundary states and the development of topological insulators in practical applications.

Localized photonic states and dynamic process in nonreciprocal coupled Su-Schrieffer-Heeger chain

We investigate the localized photonic states and dynamic process in one-dimensional nonreciprocal coupled Su-Schrieffer-Heeger chain. Through numerical calculation of energy eigenvalue spectrum and state distributions of the system, we find that different localized photonic states with special energy eigenvalues can be induced by the nonreciprocal coupling, such as zero-energy edge states, interface states and bound states with pure imaginary energy eigenvalues. Moreover, we analyze the dynamic process of photonic states in such non-Hermitian system. Interestingly, it is shown that the nonreciprocal coupling has an evident gathering effect on the photons, which also break the trapping effect of topologically protected edge states. In addition, we consider the impacts of on-site defect potentials on the dynamic process of photonic states for the system. It is indicated that the photons go around the defect lattice site and still present the gathering effect, and different forms of laser pulses can be induced with the on-site defect potentials in different lattice sites. Furthermore, we present the method for the quantum simulation of current model based on the circuit quantum electrodynamic lattice.

Exceptional non-Hermitian topological edge mode and its application to active matter

Topological materials exhibit edge-localized scattering-free modes protected by their nontrivial bulk topology through the bulk-edge correspondence in Hermitian systems. While topological phenomena have recently been much investigated in non-Hermitian systems with dissipations and injections, the fundamental principle of their edge modes has not fully been established. Here, we reveal that, in non-Hermitian systems, robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, thus indicating the breakdown of the bulk-edge correspondence. The robustness of these edge modes originates from yet another topological structure accompanying the branchpoint singularity around an exceptional point, at which eigenvectors coalesce and the Hamiltonian becomes nondiagonalizable. Their characteristic complex eigenenergy spectra are applicable to realize lasing wave packets that propagate along the edge of the sample. We numerically confirm the emergence and the robustness of the proposed edge modes in the prototypical lattice models. Furthermore, we show that these edge modes appear in a model of chiral active matter based on the hydrodynamic description, demonstrating that active matter can exhibit an inherently non-Hermitian topological feature. The proposed general mechanism would serve as an alternative designing principle to realize scattering-free edge current in non-Hermitian devices, going beyond the existing frameworks of non-Hermitian topological phases.