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 explore the possibilities for constructing Lagrangian descriptions of threedimensional superconformal classical gauge theories that contain a Chern-Simons term, but no kinetic term, for the gauge fields. Classes of such theories with N = 1 and N = 2 supersymmetry are found. However, interacting theories of this type with N = 8 supersymmetry do not exist.

Topological insulators are phases of matter characterized by topological edge states that propagate in a unidirectional manner that is robust to imperfections and disorder. These attributes make topological insulator systems ideal candidates for enabling applications in quantum computation and spintronics. We propose a concept that exploits topological effects in a unique way: the topological insulator laser. These are lasers whose lasing mode exhibits topologically protected transport without magnetic fields. The underlying topological properties lead to a highly efficient laser, robust to defects and disorder, with single-mode lasing even at very high gain values. The topological insulator laser alters current understanding of the interplay between disorder and lasing, and at the same time opens exciting possibilities in topological physics, such as topologically protected transport in systems with gain. On the technological side, the topological insulator laser provides a route to arrays of semiconductor lasers that operate as one single-mode high-power laser coupled efficiently into an output port.

Topological insulators are a striking example of materials in which topological invariants are manifested in robustness against perturbations [1,2]. Their most prominent feature is the emergence of topological edge states with reduced dimension at the boundary between areas with distinct topological invariants. The observable physical effect is unidirectional robust transport, unaffected by defects or disorder. Topological insulators were originally observed in the integer quantum Hall effect [3], and subsequently suggested [4-6] and observed [7] even in the absence of magnetic field. These were fermionic systems of correlated electrons. However, during the past decade the concepts of topological physics have been introduced into numerous fields beyond condensed matter, ranging from microwaves [8,9] and photonic systems [10-12] to cold atoms [13,14], acoustics [15,16] and even mechanics [17,18]. Recently, topological insulators were proposed [19-21] in exciton-polariton systems organized as honeycomb (graphene-like) lattices, under the influence of a magnetic field. Topological phenomena in polaritons are fundamentally different from all topological effects demonstrated experimentally thus far: exciton-polaritons are part-light part-matter quasiparticles emerging from the strong coupling of quantum well excitons and cavity photons [22]. Here, we demonstrate experimentally the first exciton-polariton topological insulator. This constitutes the first symbiotic light-matter topological insulators. Our polariton lattice is excited non-resonantly, and the chiral topological polariton edge mode is populated by a polariton condensation mechanism. We use scanning imaging techniques in real-space and in Fourier-space to measure photoluminescence, and demonstrate that the topological edge mode avoids defects, and that the propagation direction of the mode can be reversed by inverting the applied magnetic field. Our exciton-polariton topological insulator paves the way for a variety of new topological phenomena, as they involve light-matter interaction, gain, and perhaps most importantly -exciton-polaritons interact with one another as a nonlinear many-body system.Microcavity exciton-polaritons (polaritons) are composite bosons originating from the strong coupling of quantum well excitons to microcavity photons. While the excitonic fraction provides a strong non-linearity, the photonic part results in a low effective mass, allowing the formation of a driven-dissipative Bose-Einstein condensate [23,24] and a superfluid phase [25], making polaritons being referred to as "quantum fluids of light" [26]. For the epitaxially well-controlled III-V semiconductor material system, a variety of techniques are available to micropattern such cavities in order to precisely engineer the potential landscapes of polaritons [27]. With the recent advances of bringing topological effects to the realms of photonics [8][9][10][11][12]28], several avenues to realize topological edge propagation with polaritons have been suggested [19][20][21], wi...

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.