Nonreciprocal Transport of Exciton Polaritons in a Non-Hermitian Chain

Localization of Chiral Edge States by the Non-Hermitian Skin Effect

Quantum Hall systems host chiral edge states extending along the one-dimensional boundary of any two-dimensional sample. In solid state materials, the edge states serve as perfectly robust transport channels that produce a quantized Hall conductance; due to their chirality, and the topological protection by the Chern number of the bulk band structure, they cannot be spatially localized by defects or disorder. Here, we show experimentally that the chiral edge states of a lossy quantum Hall system can be localized. In a gyromagnetic photonic crystal exhibiting the quantum Hall topological phase, an appropriately structured loss configuration imparts the edge states' complex energy spectrum with a feature known as point-gap winding. This intrinsically non-Hermitian topological invariant is distinct from the Chern number invariant of the bulk (which remains intact) and induces mode localization via the "non-Hermitian skin effect." The interplay of the two topological phenomena-the Chern number and point-gap winding-gives rise to a non-Hermitian generalization of the paradigmatic Chern-type bulk-boundary correspondence principle. Compared to previous realizations of the non-Hermitian skin effect, the skin modes in this system have superior robustness against local defects and disorders.

Nonlinear Exceptional Points with a Complete Basis in Dynamics

Exceptional points (EPs) are special spectral singularities at which two or more eigenvalues, and their corresponding eigenvectors, coalesce and become identical. In conventional wisdom, the coalescence of eigenvectors inevitably leads to the loss of completeness of the eigenbasis. Here, we show that this scenario breaks down in general at nonlinear EPs (NEPs). As an example, we realize a fifth-order NEP (NEP_{5}) within only three coupled resonators with both a theoretical model and simulations in circuits. One stable and another four auxiliary steady eigenstates of the nonlinear Hamiltonian coalesce at the NEP_{5}, and the response of eigenfrequency to perturbations demonstrates a fifth-order root law. Intriguingly, the biorthogonal eigenbasis of the Hamiltonian governing the system dynamics is still complete, and this fact is corroborated by a finite Petermann factor instead of a divergent one at conventional EPs. Consequently, the amplification of noise, which diverges at other EPs, converges at our NEP_{5}. Our finding transforms the understanding of EPs and shows potential for miniaturizing various key applications operating near EPs.

Simulation of Interaction-Induced Chiral Topological Dynamics on a Digital Quantum Computer

Chiral edge states are highly sought after as paradigmatic topological states relevant to both quantum information processing and dissipationless electron transport. Using superconducting transmon-based quantum computers, we demonstrate chiral topological propagation that is induced by suitably designed interactions, instead of flux or spin-orbit coupling. Also different from conventional 2D realizations, our effective Chern lattice is implemented on a much smaller equivalent 1D spin chain, with sequences of entangling gates encapsulating the required time-reversal breaking. By taking advantage of the quantum nature of the platform, we circumvented difficulties from the limited qubit number and gate fidelity in present-day noisy intermediate-scale quantum era quantum computers, paving the way for the quantum simulation of more sophisticated topological states on very rapidly developing quantum hardware.

Direct measurement of a non-Hermitian topological invariant in a hybrid light-matter system

Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterized by topological invariants. In energy-conserving (Hermitian) systems, these invariants are determined by the winding of eigenstates in momentum space. In non-Hermitian systems, a topological invariant is predicted to emerge from the winding of the complex eigenenergies. Here, we directly measure the non-Hermitian topological invariant arising from exceptional points in the momentum-resolved spectrum of exciton polaritons. These are hybrid light-matter quasiparticles formed by photons strongly coupled to electron-hole pairs (excitons) in a halide perovskite semiconductor at room temperature. We experimentally map out both the real (energy) and imaginary (linewidth) parts of the spectrum near the exceptional points and extract the novel topological invariant—fractional spectral winding. Our work represents an essential step toward realization of non-Hermitian topological phases in a condensed matter system.

Acoustic non-Hermitian skin effect from twisted winding topology

The recently discovered non-Hermitian skin effect (NHSE) manifests the breakdown of current classification of topological phases in energy-nonconservative systems, and necessitates the introduction of non-Hermitian band topology. So far, all NHSE observations are based on one type of non-Hermitian band topology, in which the complex energy spectrum winds along a closed loop. As recently characterized along a synthetic dimension on a photonic platform, non-Hermitian band topology can exhibit almost arbitrary windings in momentum space, but their actual phenomena in real physical systems remain unclear. Here, we report the experimental realization of NHSE in a one-dimensional (1D) non-reciprocal acoustic crystal. With direct acoustic measurement, we demonstrate that a twisted winding, whose topology consists of two oppositely oriented loops in contact rather than a single loop, will dramatically change the NHSE, following previous predictions of unique features such as the bipolar localization and the Bloch point for a Bloch-wave-like extended state. This work reveals previously unnoticed features of NHSE, and provides the observation of physical phenomena originating from complex non-Hermitian winding topology.

Non-Hermitian skin effect fundamentally challenges the conventional topological description of a system. Here the authors demonstrate a bipolar non-Hermitian skin effect, where bulk eigenstates localize towards two directions, in a one-dimensional non-reciprocal acoustic crystal with twisted topology.

Quantum fluids of light in all-optical scatterer lattices

One of the recently established paradigms in condensed matter physics is examining a system's behaviour in artificial potentials, giving insight into phenomena of quantum fluids in hard-to-reach settings. A prominent example is the matter-wave scatterer lattice, where high energy matter waves undergo transmission and reflection through narrow width barriers leading to stringent phase matching conditions with lattice band formation. In contrast to evanescently coupled lattice sites, the realisation of a scatterer lattice for macroscopic matter-wave fluids has remained elusive. Here, we implement a system of exciton-polariton condensates in a non-Hermitian Lieb lattice of scatterer potentials. By fine tuning the lattice parameters, we reveal a nonequilibrium phase transition between distinct regimes of polariton condensation: a scatterer lattice of gain guided polaritons condensing on the lattice potential maxima, and trapped polaritons condensing in the potential minima. Our results pave the way towards unexplored physics of non-Hermitian fluids in non-stationary mixtures of confined and freely expanding waves.

Conjugated topological interface-states in coupled ring resonators

The optical properties of topological photonics have attracted much interest recently because its potential applications for robust unidirectional transmission that are immune to scattering at disorder. However, researches on topological series coupled ring resonators (T-SCRR) have been much less discussed. The existence of topological interface-states (TIS) in the T-SCRR is described for the first time in this article. An approach has been developed to achieve this goal via the band structure of dielectric binary ring resonators and the Zak phase of each bandgap. It is found that an ultra-high-Q with complete transmission is obtained by the conjugated topological series coupled ring resonators due to the excitation of conjugated topological interface-states, which is different from those in conventional TIS. Furthermore, the problem of transmission decreases resulting from high-Q increases in the traditional photonic system is significantly improved by this approach. These findings could pave a novel path for developing advanced high-Q filters, optical sensors, switches, resonators, communications and quantum information processors.