Observation of π/2 Modes in an Acoustic Floquet System

Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems

We present a pedagogical review of the periodically driven non-Hermitian systems, particularly on the rich interplay between the non-Hermitian skin effect and the topology. We start by reviewing the non-Bloch band theory of the static non-Hermitian systems and discuss the establishment of its generalized bulk-boundary correspondence (BBC). Ultimately, we focus on the non-Bloch band theory of two typical periodically driven non-Hermitian systems: harmonically driven non-Hermitian system and periodically quenched non-Hermitian system. The non-Bloch topological invariants were defined on the generalized Brillouin zone and the real space wave functions to characterize the Floquet non-Hermtian topological phases. Then, the generalized BBC was established for the two typical periodically driven non-Hermitian systems. Additionally, we review novel phenomena in the higher-dimensional periodically driven non-Hermitian systems, including Floquet non-Hermitian higher-order topological phases and Floquet hybrid skin-topological modes. The experimental realizations and recent advances have also been surveyed. Finally, we end with a summarization and hope this pedagogical review can motivate further research on Floquet non-Hermtian topological physics.

Dynamical Detection of Topological Spectral Density

Local density of states (LDOS) is emerging as powerful means of exploring classical-wave topological phases. However, the current LDOS detection method remains rare and merely works for static situations. Here, we introduce a generic dynamical method to detect both the static and Floquet LDOS, based on an elegant connection between dynamics of chiral density and local spectral densities. Moreover, we find that the Floquet LDOS allows to measure out Floquet quasienergy spectra and identify topological π modes. As an example, we demonstrate that both the static and Floquet higher-order topological phase can be universally identified via LDOS detection, regardless of whether the topological corner modes are in energy gaps, bands, or continuous energy spectra without band gaps. Our study opens a new avenue utilizing dynamics to detect topological spectral densities and provides a universal approach of identifying static and Floquet topological phases.

Nonlocal effective medium theory for phononic temporal metamaterials

We have developed a nonlocal effective medium theory (EMT) for phononic temporal metamaterials using the multiscale technique. Our EMT yields closed-form expressions for effective constitutive parameters and reveals these materials as reciprocal media with symmetric band dispersion. Even without spatial symmetry breaking, nonzero Willis coupling coefficients emerge with time modulation and broken time-reversal symmetry, when the nonlocal effect is taken into account. Compared to the local EMT, our nonlocal version is more accurate for calculating the bulk band at high wavenumbers and essential for understanding nonlocal effects at temporal boundaries. This nonlocal EMT can be a valuable tool for studying and designing phononic temporal metamaterials beyond the long-wavelength limit.

Observation of π solitons in oscillating waveguide arrays

Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous π modes of topological origin despite the fact that the lattice spends only half of the evolution period in topologically nontrivial phase, while during other half-period it is topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from periodically oscillating waveguides inscribed in transparent nonlinear optical medium, we report experimental observation of photonic anomalous π modes residing at the edge or in the corner of the one- or two-dimensional arrays, respectively, and demonstrate a new class of topological π solitons bifurcating from such modes in the topological gap of the Floquet spectrum at high powers. π solitons reported here are strongly oscillating nonlinear Floquet states exactly reproducing their profiles after each longitudinal period of the structure. They can be dynamically stable in both one- and two-dimensional oscillating waveguide arrays, the latter ones representing the first realization of the Floquet photonic higher-order topological insulator, while localization properties of such π solitons are determined by their power.

Non-Hermitian Floquet Topological Matter-A Review

The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matter due to its exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. We first give a bird's-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties. With the aid of these tools, we present typical examples of non-Hermitian Floquet topological insulators, superconductors, and quasicrystals, with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties, and localization transitions. We conclude this review by summarizing our main findings and presenting our vision of future directions.

Observation of delocalization transition in topological waveguide arrays with long-range interactions

Topological edge states are a generic feature of topological insulators, and the long-range interactions, which break certain properties of topological edge states, are always non-negligible in real physical systems. In this Letter, we investigate the influence of next-nearest-neighbor (NNN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) model by extracting the survival probabilities at the boundary of the photonic lattices. By introducing a series of integrated photonic waveguide arrays with different strengths of long-range interactions, we experimentally observe delocalization transition of light in SSH lattices with nontrivial phase, which is in good agreement with our theoretical predictions. The results indicate that the NNN interactions can significantly affect the edge states, and that the localization of these states can be absent in topologically nontrivial phase. Our work provides an alternative way to investigate the interplay between long-range interactions and localized states, which may stimulate further interest in topological properties in relevant structures.