We demonstrate generation of chiral modes -vortex flows with fixed handedness in excitonpolariton quantum fluids. The chiral modes arise in the vicinity of exceptional points (non-Hermitian spectral degeneracies) in an optically-induced resonator for exciton polaritons. In particular, a vortex is generated by driving two dipole modes of the non-Hermitian ring resonator into degeneracy. Transition through the exceptional point in the space of the system's parameters is enabled by precise manipulation of real and imaginary parts of the closed-wall potential forming the resonator. As the system is driven to the vicinity of the exceptional point, we observe the formation of a vortex state with a fixed orbital angular momentum (topological charge). Our method can be extended to generate high-order orbital angular momentum states through coalescence of multiple non-Hermitian spectral degeneracies, which could find application in integrated optoelectronics.Introduction. Exceptional points in wave resonators of different origin arise when both spectral positions and linewidths of two resonances coincide and the corresponding spatial modes coalesce into one [1,2]. Originally identified as an inherent property of non-Hermitian quantum systems [3][4][5], exceptional points have become a focus of intense research in classical systems with gain and loss [6], such as optical cavities [7], microwave resonators [8,15], and plasmonic nanostructures [9]. The counterintuitive behaviour of a wave system in the vicinity of an exceptional point led to demonstrations of a range of peculiar phenomena, including enhanced loss-assisted lasing [10,11], unidirectional transmission of signals [12], and loss-induced transparency [13].Due to the nontrivial topology of the exceptional point, the two eigenstates coalesce with a phase difference of ± π/2, which results in a well-defined handedness (chirality) of the surviving eigenstate [14]. This remarkable property of the eigenstate at the exceptional point was first experimentally demonstrated in a microwave cavity [15] and, very recently, led to observation of directional lasing in optical micro-resonators [16,17]. So far, the chirality of the unique eigenstate at an exceptional point has not been demonstrated in any quantum system.In this work, we demonstrate formation of a chiral state at an exceptional point in a macroscopic quantum system of condensed exciton polaritons. Exciton polaritons are hybrid light-matter bosonic quasiparticles arising due to strong coupling between excitons and photons in semiconductor microcavities [18,19]. Once sufficient density of exciton polaritons is injected by an optical or electrical pump, the transition to quantum degeneracy occurs, whereby typical signatures of a Bose-Einstein con-

We present a scheme of interaction-induced topological bandstructures based on the spin anisotropy of exciton-polaritons in semiconductor microcavities. We predict theoretically that this scheme allows the engineering of topological gaps, without requiring a magnetic field or strong spinorbit interaction (transverse electric-transverse magnetic splitting). Under non-resonant pumping, we find that an initially topologically trivial system undergoes a topological transition upon the spontaneous breaking of phase symmetry associated with polariton condensation. Under resonant coherent pumping, we find that it is also possible to engineer a topological dispersion that is linear in wavevector -a property associated with polariton superfluidity. The hybridization of light and matter in the form of exciton-polaritons in microcavities has led to a new kind of quantum fluid 1 , well-known for its ability to develop coherence spontaneously as a Bose-Einstein condensate 2,3 and flow without friction as a superfluid 4,5 , even at room temperature 6 . Furthermore it has been shown that exciton-polaritons can be manipulated by highly tuneable optically-induced potentials 7,8 . These allow introducing a spatial structure in an otherwise homogeneous system, which has given access to a variety of fundamental effects, including: the gating 9,10 and routing 11,12 of polariton flow; the trapping of polariton superfluids 13,14 ; the formation of patterns 15 ; the breaking of chiral symmetry 16 ; and the exposure of exceptional points 17 .Taking inspiration from the field of topological photonics 18 , recent theoretical works have considered engineering topological polariton bandstructures [19][20][21][22] . These are characterized by the formation of chiral edge states, at the boundaries between areas with different topology, which exhibit uni-directional propagation and an absence of backscattering even in the presence of defects or disorder. Due to these properties, chiral edge states are highly relevant to the field of polaritonics, which seeks robust mechanisms of propagating fields between individual information processing elements to allow for cascadable systems 23,24 . The presence of Kerr-type interactions between polaritons would also allow the development of a nonlinear topological photonics, where schemes for solitons forming in the chiral edge modes have also appeared in recent theoretical works [25][26][27] .The previous schemes of topological polaritons have been based on three ingredients. First, a periodic potential is required to introduce the bandstructure on which to impose non-trivial topology. This has implicated the need for hard engineering of the polariton potential, such as is achieved by etching micropillar arrays 28 . Second, so that edge states propagate in only one direction, timereversal symmetry should be broken, which implies the application of a magnetic field. Third, a significant amount of spin-orbit coupling is needed, which implies strong transverse electric-transverse magnetic (TE-TM) splitting....

We propose using the effective spin-orbit coupling of light in Bragg-modulated cylindrical waveguides for the efficient separation of spin-up and spin-down photons emitted by a single photon emitter. Because of the spin and directional dependence of photonic stop bands in the waveguides, spin-up (-down) photon propagation in the negative (positive) direction along the waveguide axis is blocked while the same photon freely propagates in the opposite direction. Frequency shifts of photonic band structures induced by the spin-orbit coupling are verified by finite-difference time-domain numerical simulations.