Physical systems exhibiting topological invariants are naturally endowed with robustness against perturbations, as manifested in topological insulators-materials exhibiting robust electron transport, immune from scattering by defects and disorder. Recent years have witnessed intense efforts toward exploiting these phenomena in photonics. Here we demonstrate a nonmagnetic topological insulator laser system exhibiting topologically protected transport in the cavity. Its topological properties give rise to single-mode lasing, robustness against defects, and considerably higher slope efficiencies compared to the topologically trivial counterparts. We further exploit the properties of active topological platforms by assembling the system from -chiral microresonators, enforcing predetermined unidirectional lasing without magnetic fields. This work paves the way toward active topological devices with exciting properties and functionalities.

We report the first observation of lasing topological edge states in a 1D Su-Schrieffer-Heeger active array of microring resonators. We show that the judicious use of non-Hermiticity can promote single edge-mode lasing in such arrays. Our experimental and theoretical results demonstrate that, in the presence of chiral-time symmetry, this non-Hermitian topological structure can experience phase transitions that are dictated by a complex geometric phase. Our work may pave the way towards understanding the fundamental aspects associated with the interplay among non-Hermiticity, nonlinearity, and topology in active systems.

In the past few years, concepts from non-Hermitian (NH) physics, originally developed within the context of quantum field theories, have been successfully deployed over a wide range of physical settings where wave dynamics are known to play a key role. In optics, a special class of NH Hamiltonians – which respects parity-time symmetry – has been intensely pursued along several fronts. What makes this family of systems so intriguing is the prospect of phase transitions and NH singularities that can in turn lead to a plethora of counterintuitive phenomena. Quite recently, these ideas have permeated several other fields of science and technology in a quest to achieve new behaviors and functionalities in nonconservative environments that would have otherwise been impossible in standard Hermitian arrangements. Here, we provide an overview of recent advancements in these emerging fields, with emphasis on photonic NH platforms, exceptional point dynamics, and the very promising interplay between non-Hermiticity and topological physics.

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Non-Hermitian exceptional points (EPs) represent a special type of degeneracy where not only the eigenvalues coalesce, but also the eigenstates tend to collapse on each other. Recent studies have shown that, in the presence of an EP, light–matter interactions are profoundly modified, leading to a host of unexpected optical phenomena ranging from enhanced sensitivity to chiral light transport. Here we introduce a family of unidirectional resonators based on a novel type of broadband exceptional points. In active settings, the resulting unidirectionality exhibits resilience to perturbations, thus, providing a robust and tunable approach for directly generating beams with distinct orbital angular momenta (OAM). This work could open up new possibilities for manipulating OAM degrees of freedom in applications pertaining to telecommunications and quantum information sciences, while at the same time may expand the notions of non-Hermiticity in the orbital angular momentum space.

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The ability to tailor the hopping interactions between the constituent elements of a physical system could enable the observation of unusual phenomena that are otherwise inaccessible in standard settings 1,2 . In this regard, a number of recent theoretical studies have indicated that an asymmetry in either the short-or long-range complex exchange constants can lead to counterintuitive effects, for example, the possibility of a Kramer's degeneracy even in the absence of spin 1/2 or the breakdown of the bulk-boundary correspondence [3][4][5][6][7][8] . Here, we show how such tailored asymmetric interactions can be realized in photonic integrated platforms by exploiting non-Hermitian concepts, enabling a class of topological behaviors induced by optical gain. As a demonstration, we implement the Haldane model, a canonical lattice that relies on asymmetric long-range hopping in order to exhibit quantum Hall behavior without a net external magnetic flux. The topological response observed in this lattice is a result of gain and vanishes in a passive but otherwise identical structure. Our findings not only enable the realization of a wide class of non-trivial phenomena associated with tailored interactions, but also opens up avenues to study the role of gain and nonlinearity in topological systems in the presence of quantum noise.

†These authors contributed equally to this work.Spin models arise in the microscopic description of magnetic materials, where the macroscopic characteristics are governed by exchange interactions among the constituent magnetic moments. Recently, there has been a growing interest in complex systems with spin Hamiltonians1-3 -largely due to the rich behaviors exhibited by such interactions at the macroscale. Along these lines, it has been shown that certain classes of optimization problems involving large degrees of freedom can be effectively mapped into classical spin models. In this vein, the respective extremum can be found by identifying the ground state of the associated spin Hamiltonian. Here, we show both theoretically and experimentally, that the cooperative interplay among vectorial electromagnetic modes in coupled metallic nanolasers4-7 can be utilized as a means to emulate certain types of spin-like systems. The ensuing spin exchange interactions are in general anisotropic, in a way similar to that encountered in magnetic materials involving spin-orbit coupling. For some topologies, we find that these active nanophotonic structures are governed by a classical XY Hamiltonian that exhibits two phases akin to those associated with ferromagnetic (FM) and antiferromagnetic (AF) materials. In addition, we show that in certain configurations, the electromagnetic field distribution can undergo geometrical frustration, depending on the lattice shape and the transverse resonant modes supported by the individual cavity elements. Our results could pave the way towards a new scalable nanophotonic platform to study spin exchange interactions, that can in turn be potentially exploited to investigate more large-scale networks, emulate some magnetic materials, or to address a variety of optimization problems.Spin Hmailtonians arise in a ubiquitous manner in nature. Over the years, such models have been a subject of intense investigation in many and diverse areas of science and technology, ranging from condensed matter physics8 and spintronics9 to quantum information theory3. Of particular interest is geometric frustration that occurs when a certain type of local order, associated with a minimum energy state, cannot extend throughout a system due to geometrical constraints10. This effect appears in a variety of physical problems and settings, ranging from residual entropy in water11 and spin ice12,13, to orbital exchange in Mott insulators14 and the emergence of the blue phases in cholesteric liquid crystals15. In magnetic materials, frustration is typically associated with a set of highly degenerate ground states of a spin Hamiltonian, which in turn leads to complex macroscopic behaviors such as those observed in spin-liquid or spin-ice phases16.