Robust Zero Modes in Non-Hermitian Systems without Global Symmetries.

We present an approach to achieve zero modes in lattice models that do not rely on any symmetry or topology of the bulk, which are robust against disorder in the bulk of any type and strength. Such symmetry-free zero modes (SFZMs) are formed by attaching a single site or small cluster with zero mode(s) to the bulk, which serves as the "nucleus" that expands to the entire lattice. We identify the requirements on the couplings between this boundary and the bulk, which reveals that this approach is intrinsically non-Hermitian. We then provide several examples with either an arbitrary or structured bulk, forming spectrally embedded zero modes in the bulk continuum, midgap zero modes, and even restoring the "zeroness" of coupling or disorder-shifted topological corner states. Focusing on viable realizations using photonic lattices, we show that the resulting SFZM can be observed as the single lasing mode when optical gain is applied to the boundary.

Non-Hermiticity-Governed Active Photonic Resonances.

Photonic resonances play an essential role in the generation and propagation of light in optical and photonic devices, as well as in light-matter interaction, including nonlinear optical responses. Previous studies in lasers and other open systems have shown exotic roles played by non-Hermiticity on modifying passive resonances, defined in the absence of optical gain and loss. Here we report a new type of resonances in non-Hermitian photonic systems that does not originate from a passive resonance, identified by analyzing a unique quantization condition in the non-Hermitian extension of the Wentzel-Kramers-Brillouin method. Termed active photonic resonances, these unique resonances are found in non-Hermitian systems with a spatially correlated complex dielectric function, which is related to supersymmetry quantum mechanics after a Wick rotation. Remarkably, such an active photonic resonance shifts continuously on the real frequency axis as optical gain increases, suggesting the possibility of a tunable on-chip laser that can span a wavelength range over 100 nm.

Pseudochirality: A Manifestation of Noether's Theorem in Non-Hermitian Systems.

Noether's theorem relates constants of motion to the symmetries of the system. Here we investigate a manifestation of Noether's theorem in non-Hermitian systems, where the inner product is defined differently from quantum mechanics. In this framework, a generalized symmetry that we term pseudochirality emerges naturally as the counterpart of symmetries defined by a commutation relation in quantum mechanics. Using this observation, we reveal previously unidentified constants of motion in non-Hermitian systems with parity-time and chiral symmetries. We further elaborate the disparate implications of pseudochirality induced constant of motion: It signals the pair excitation of a generalized "particle" and the corresponding "hole" but vanishes universally when the pseudochiral operator is antisymmetric. This disparity, when manifested in a non-Hermitian topological lattice with the Landau gauge, depends on whether the lattice size is even or odd. We further discuss previously unidentified symmetries of this non-Hermitian topological system, and we reveal how its constant of motion due to pseudochirality can be used as an indicator of whether a pure chiral edge state is excited.