Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as for fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (that is, non-Hermitian) quantum system, which requires constant pumping of energy and continuously decays, releasing coherent radiation. Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and loss. However, the inherent non-Hermitian nature of this potential has so far been largely ignored in exciton-polariton physics. Here we demonstrate that non-Hermiticity dramatically modifies the structure of modes and spectral degeneracies in exciton-polariton systems, and, therefore, will affect their quantum transport, localization and dynamical properties. Using a spatially structured optical pump, we create a chaotic exciton-polariton billiard--a two-dimensional area enclosed by a curved potential barrier. Eigenmodes of this billiard exhibit multiple non-Hermitian spectral degeneracies, known as exceptional points. Such points can cause remarkable wave phenomena, such as unidirectional transport, anomalous lasing/absorption and chiral modes. By varying parameters of the billiard, we observe crossing and anti-crossing of energy levels and reveal the non-trivial topological modal structure exclusive to non-Hermitian systems. We also observe mode switching and a topological Berry phase for a parameter loop encircling the exceptional point. Our findings pave the way to studies of non-Hermitian quantum dynamics of exciton-polaritons, which may uncover novel operating principles for polariton-based devices.

Bosonic condensates of exciton polaritons (light-matter quasiparticles in a semiconductor) provide a solid-state platform for studies of non-equilibrium quantum systems with a spontaneous macroscopic coherence. These driven, dissipative condensates typically coexist and interact with an incoherent reservoir, which undermines measurements of key parameters of the condensate. Here, we overcome this limitation by creating a high-density exciton-polariton condensate in an opticallyinduced box trap. In this so-called Thomas-Fermi regime, the condensate is fully separated from the reservoir and its behaviour is dominated by interparticle interactions. We use this regime to directly measure the polariton-polariton interaction strength, and reduce the existing uncertainty in its value from four orders of magnitude to within three times the theoretical prediction. The Thomas-Fermi regime has previously been demonstrated only in ultracold atomic gases in thermal equilibrium. In a non-equilibrium exciton-polariton system, this regime offers a novel opportunity to study interaction-driven effects unmasked by an incoherent reservoir.

A non-Hermitian topological invariant arising from exceptional points is directly probed in an exciton-polariton system.

The property of superfluidity, first discovered in liquid 4 He, is closely related to the Bose--Einstein condensation (BEC) of interacting bosons 1 . However, even at zero temperature, when the whole bosonic quantum liquid would become superfluid, only a fraction of it would remain Bose--condensed at zero momentum 2 . This is due to quantum depletion phenomenon, whereby particles are excited to larger momenta states due to interparticle interactions and quantum fluctuations. Quantum depletion of weakly interacting atomic BECs in thermal equilibrium is well understood theoretically 3 but is difficult to measure 4-7 . Driven--dissipative systems, such as condensates of exciton--polaritons (photons coupled to electron--hole pairs in a semiconductor) are even more challenging, since their nonequilibrium nature is predicted to suppress quantum depletion 8 . Here, we observe quantum depletion of an optically trapped 9 high--density exciton--polariton condensate 10,11 by directly detecting the spectral branch of elementary excitations populated by this process. Analysis of the population of this branch in momentum space shows that quantum depletion of an exciton--polariton condensate can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the fraction of matter (exciton) in an exciton--polariton. Our results reveal the effects of exciton-polariton interactions beyond the mean--field description and call for a deeper understanding of the relationship between equilibrium and nonequilibrium BECs.

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 study the loading of a nonequilibrium, dissipative system of composite bosons -exciton polaritons -into a one dimensional periodic lattice potential. Utilizing momentum resolved photoluminescence spectroscopy, we observe a transition between an incoherent Bose gas and a polariton condensate, which undergoes further transitions between different energy states in the band-gap spectrum of the periodic potential with increasing pumping power. We demonstrate controlled loading into distinct energy bands by modifying the size and shape of the excitation beam. The observed effects are comprehensively described in the framework of a nonequilibrium model of polariton condensation. In particular, we implement a stochastic treatment of quantum and thermal fluctuations in the system and confirm that polariton-phonon scattering is a key energy relaxation mechanism enabling transitions from the highly nonequilibrium polariton condensate in the gap to the ground band condensation for large pump powers.Introduction.-Since the initial demonstration of Bose-Einstein condensation of microcavity exciton polaritons [1], one particular direction of research has been focused on engineering the potential landscape of polaritons. These potentials have been created by deposition of metal on the microcavity surface [2], interference of surface acoustic waves [3], deep etching of micropillars [4], fabrication of shallow mesas [5], and deposition of semiconductor micro-rods on a silicon grating [6]. Periodic arrangements of these potentials have been used to study the formation of gap solitons [7,8] and graphene-like band spectra (including Dirac cones) [4,9], are predicted to be prime candidates for the generation of topological polariton states [10][11][12], and hold high promise for implementation of quantum simulators in solid state systems [13].

Atomically thin transition metal dichalcogenide crystals (TMDCs) have extraordinary optical properties that make them attractive for future optoelectronic applications. Integration of TMDCs into practical all‐dielectric heterostructures hinges on the ability to passivate and protect them against necessary fabrication steps on large scales. Despite its limited scalability, encapsulation of TMDCs in hexagonal boron nitride (hBN) currently has no viable alternative for achieving high performance of the final device. Here, it is shown that the novel, ultrathin Ga2O3 glass is an ideal centimeter‐scale coating material that enhances optical performance of the monolayers and protects them against further material deposition. In particular, Ga2O3 capping of monolayer WS2 outperforms commercial‐grade hBN in both scalability and optical performance at room temperature. These properties make Ga2O3 highly suitable for large‐scale passivation and protection of monolayer TMDCs in functional heterostructures.

A bosonic condensate of exciton polaritons in a semiconductor microcavity is a macroscopic quantum state subject to pumping and decay. The fundamental nature of this driven-dissipative condensate is still under debate. Here, we gain an insight into spontaneous condensation by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in a single-shot optical excitation regime, without averaging over multiple condensate realisations. We demonstrate that condensation is strongly influenced by an incoherent reservoir and that the reservoir depletion, the so-called spatial hole burning, is critical for the transition to the ground state. Condensates of photon-like polaritons exhibit strong shot-to-shot fluctuations and density filamentation due to the effective self-focusing associated with the reservoir depletion. In contrast, condensates of exciton-like polaritons display smoother spatial density distributions and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study fundamental properties of non-equilibrium condensation in the presence of a reservoir.