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 report on the experimental observation of the nonlinear analogue of the optical spin Hall effect under highly nonresonant circularly polarized excitation of an exciton-polariton condensate in a GaAs/AlGaAs microcavity. The circularly polarized polariton condensates propagate over macroscopic distances, while the collective condensate spins coherently precess around an effective magnetic field in the sample plane performing up to four complete revolutions.

We investigate the spin dynamics of polariton condensates spatially separated from and effectively confined by the pumping exciton reservoir. We obtain a strong correlation between the ellipticity of the non-resonant optical pump and the degree of circular polarisation (DCP) of the condensate at the onset of condensation. With increasing excitation density we observe a reversal of the DCP. The spin dynamics of the trapped condensate are described within the framework of the spinor complex Ginzburg-Landau equations in the Josephson regime, where the dynamics of the system are reduced to a current-driven Josephson junction. We show that the observed spin reversal is due to the interplay between an internal Josephson coupling effect and the detuning of the two projections of the spinor condensate via transition from a synchronised to a desynchronised regime. These results suggest that spinor polariton condensates can be controlled by tuning the non-resonant excitation density offering applications in electrically pumped polariton spin switches.

We investigate the propagation and scattering of polaritons in a planar GaAs microcavity in the linear regime under resonant excitation. The propagation of the coherent polariton wave across an extended defect creates phase and intensity patterns with identical qualitative features previously attributed to dark and half-dark solitons of polaritons. We demonstrate that these features are observed for negligible nonlinearity (i.e., polariton-polariton interaction) and are, therefore, not sufficient to identify dark and half-dark solitons. A linear model based on the Maxwell equations is shown to reproduce the experimental observations. PACS numbers:Solitons are solitary waves that preserve their shape while propagating through a dispersive medium [1,2] due to the compensation of the dispersion-induced broadening by the nonlinearity of the medium [3]. Over the years, spatial solitons have been observed by employing a variety of nonlinearities ranging from Kerr nonlinear media [4] to photorefractive [5] and quadratic [6] materials. Apart from their potential application in optical communications [7,8], solitons are important features of interacting Bose-Einstein condensates (BECs) and superfluids. The nonlinear properties of BECs can give rise to the formation of quantized interacting vortices and solitons, the latter resulting from the cancellation of the dispersion by interactions, for example, in atomic condensates. A special class of solitons is the so-called dark soliton, which feature a density node accompanied by a π phase jump. Since the first theoretical prediction in the context of BECs [9], dark solitons were studied and observed first in the field of nonlinear optics [10] and, then, in cold-atom BECs [11]. The experimental observation of BECs [12] and superfluidity [13,14] of exciton-polaritons, has sparked interest in the quantum-hydrodynamic properties of polariton fluids. In particular, the nucleation of solitary waves in the wake of an obstacle (i.e.

We study the polarization dynamics of a spatially expanding polariton condensate under nonresonant linearly polarized optical excitation. The spatially and temporally resolved polariton emission reveals the formation of non-trivial spin textures in the form of a quadruplet polarization pattern both in the linear and circular Stokes parameters, and an octuplet in the diagonal Stokes parameter. The continuous rotation of the polariton pseudospin vector through the condensate due to TE-TM splitting exhibits an ordered pattern of half-skyrmions associated with a half-integer topological number. A theoretical model based on a driven-dissipative Gross-Pitaevskii equation coupled with an exciton reservoir describes the dynamics of the nontrivial spin textures through the optical spin-Hall effect.arXiv:1602.04711v2 [physics.optics]