Several platforms are currently being explored for simulating physical systems whose complexity increases faster than polynomially with the number of particles or degrees of freedom in the system. Defects and vacancies in semiconductors or dielectric materials [1,2], magnetic impurities embedded in solid helium [3], atoms in optical lattices [4,5], photons [6], trapped ions [7,8] and superconducting q-bits [9] are among the candidates for predicting the behaviour of spin glasses, spin-liquids, and classical magnetism among other phenomena with practical technological applications. Here we investigate the potential of polariton graphs as an efficient simulator for finding the global minimum of the XY Hamiltonian. By imprinting polariton condensate lattices of bespoke geometries we show that we can simulate a large variety of systems undergoing the U(1) symmetry breaking transitions. We realise various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on unit cells of various lattices: square, triangular, linear and a disordered graph. Our results provide a route to study unconventional superfluids, spin-liquids, Berezinskii-KosterlitzThouless phase transition, classical magnetism among the many systems that are described by the XY Hamiltonian.Many properties of strongly correlated spin systems, such as spin liquids and unconventional superfluids are difficult to study as strong interactions between n particles become intractable for n as low as 30 [10]. Feynman envisioned that a quantum simulator -a special-purpose analogue processor -could be used to solve such problems [11]. It is expected that quantum simulators would lead to accurate modelling of the dynamics of chemical reactions, motion of electrons in materials, new chemical compounds and new materials that could not be obtained with classical computers using advanced numerical algorithms [12]. More generally, quantum simulators can be used to solve hard optimization problems that are at the heart of almost any multicomponent system: new materials for energy, pharmaceuticals, and photosynthesis, among others [13]. Many hard optimisation problems do not necessitate a quantum simulator as only recently realised through a network of optical parametric oscillators (OPOs) that simulated the Ising Hamiltonian of thousands of spins [14,15]. The Ising model corresponds to the n = 1 case of the n-vector model of classical unit vector spins s i with the Hamiltonian H I = − ij J ij s i · s j , where J ij is the coupling between the sites labelled i and j. For n = 2 the n-vector Hamiltonian becomes the XY Hamiltonian H XY = − ij J ij cos(θ i − θ j ), where we have parameterized unit planar vectors using the polar coordinates s i = (cos θ i , sin θ i ). Since H XY is invariant under rotation of all spins by the same angle θ i → θ i + φ the XY model is the simplest model that undergoes the U (1) symmetry-breaking transition. As such, it is used * correspondence address: pavlos.lagoudakis@soton.ac.uk to emulate Berezinskii-Kos...

We observe polariton condensation in the yellow part of the visible spectrum from a planar organic semiconductor microcavity containing the molecular dye BODIPY-Br. We provide experimental fingerprint of polariton condensation under non-resonant optical excitation, including the non-linear dependence of the emission intensity and wavelength blueshift with increasing excitation density, single excitation pulse dispersion imaging and real space interferometry. The latter two allow us to visualise the collapse of the energy distribution and the long-range coherence of the polariton condensate.

Spin-orbit interactions lead to distinctive functionalities in photonic systems. They exploit the analogy between the quantum mechanical description of a complex electronic spin-orbit system and synthetic Hamiltonians derived for the propagation of electromagnetic waves in dedicated spatial structures. We realize an artificial Rashba-Dresselhaus spin-orbit interaction in a liquid crystal–filled optical cavity. Three-dimensional tomography in energy-momentum space enabled us to directly evidence the spin-split photon mode in the presence of an artificial spin-orbit coupling. The effect is observed when two orthogonal linear polarized modes of opposite parity are brought near resonance. Engineering of spin-orbit synthetic Hamiltonians in optical cavities opens the door to photonic emulators of quantum Hamiltonians with internal degrees of freedom.

We report on the origin of energy-shifts in organic polariton condensates. The localised nature of Frenkel excitons in molecular semiconductors precludes interparticle Coulomb exchange interactionsthe latter being the dominant mechanism for blueshifts in inorganic semiconductor microcavities that bear Wannier-Mott excitons. We examine the contribution of optically induced change of the intracavity non-linear refractive index, gain induced frequency-pulling and quenching of the Rabi splitting, as well as the role of polariton-exciton and polariton-polariton scattering in the energy-shift of the polariton mode at condensation threshold in strongly coupled molecular dye microcavities. We conclude that blueshifts in organic polariton condensates arise from the interplay of the saturation of molecular optical transitions and intermolecular energy migration. Our model predicts the commonly observed step-wise increase of both the emission energy and degree of linear polarisation at polariton condensation threshold.

We report on the simultaneous observation of spontaneous symmetry breaking and long-range spatial coherence both in the strong- and the weak-coupling regime in a semiconductor microcavity. Under pulsed excitation, the formation of a stochastic order parameter is observed in polariton and photon lasing regimes. Single-shot measurements of the Stokes vector of the emission exhibit the buildup of stochastic polarization. Below threshold, the polarization noise does not exceed 10%, while above threshold we observe a total polarization of up to 50% after each excitation pulse, while the polarization averaged over the ensemble of pulses remains nearly zero. In both polariton and photon lasing regimes, the stochastic polarization buildup is accompanied by the buildup of spatial coherence. We find that the Landau criterion of spontaneous symmetry breaking and Penrose-Onsager criterion of long-range order for Bose-Einstein condensation are met in both polariton and photon lasing regimes.

Inorganic cesium lead halide perovskite nanowires, generating laser emission in the broad spectral range at room temperature and low threshold, have become powerful tools for the cutting-edge applications in the optoelectronics and nanophotonics. However, to achieve high-quality nanowires with the outstanding optical properties, it was necessary to employ long-lasting and costly methods of their synthesis, as well as postsynthetic separation and transfer procedures that are not convenient for large-scale production. Here we report a novel approach to fabricate high-quality CsPbBr3 nanolasers obtained by rapid precipitation from dimethyl sulfoxide solution sprayed onto hydrophobic substrates at ambient conditions. The synthesis technique allows producing the well-separated nanowires with a broad size distribution of 2–50 μm in 5–7 min, being the fastest method to the best of our knowledge. The formation of nanowires occurs via ligand-assisted reprecipitation triggered by intermolecular proton transfer from (CH3)2­CHOH to H2O in the presence of a minor amount of water. The XRD patterns confirm an orthorhombic crystal structure of the as-grown CsPbBr3 single nanowires. Scanning electron microscopy images reveal their regular shape and truncated pyramidal end facets, while high-resolution transmission electron microscopy ones demonstrate their single-crystal structure. The lifetime of excitonic emission of the nanowires is found to be 7 ns, when the samples are excited with energy below the lasing threshold, manifesting the low concentration of defect states. The measured nanolasers of different lengths exhibit pronounced stimulated emission above 13 μJ cm–2 excitation threshold with quality factor Q = 1017–6166. Their high performance is assumed to be related to their monocrystalline structure, low concentration of defect states, and improved end facet reflectivity.

Non-linearity and finite signal propagation speeds are omnipresent in nature, technologies, and real-world problems, where efficient ways of describing and predicting the effects of these elements are in high demand. Advances in engineering condensed matter systems, such as lattices of trapped condensates, have enabled studies on non-linear effects in manybody systems where exchange of particles between lattice nodes is effectively instantaneous. Here, we demonstrate a regime of macroscopic matter-wave systems, in which ballistically expanding condensates of microcavity exciton-polaritons act as picosecond, microscale nonlinear oscillators subject to time-delayed interaction. The ease of optical control and readout of polariton condensates enables us to explore the phase space of two interacting condensates up to macroscopic distances highlighting its potential in extended configurations. We demonstrate deterministic tuning of the coupled-condensate system between fixed point and limit cycle regimes, which is fully reproduced by time-delayed coupled equations of motion similar to the Lang-Kobayashi equation.

We observe anisotropy in the polarization flux generated in a GaAs/AlAs photonic cavity by optical illumination, equivalent to spin currents in strongly coupled microcavities. Polarization rotation of the scattered photons around the Rayleigh ring is due to the TE-TM splitting of the cavity mode. Resolving the circular polarization components of the transmission reveals a separation of the polarization flux in momentum space. These observations constitute the optical analogue of the spin Hall effect.