The effect of quantum statistics in quantum gases and liquids results in observable collective properties among many-particle systems. One prime example is Bose-Einstein condensation, whose onset in a quantum liquid leads to phenomena such as superfluidity and superconductivity. A Bose-Einstein condensate is generally defined as a macroscopic occupation of a single-particle quantum state, a phenomenon technically referred to as off-diagonal long-range order due to non-vanishing off-diagonal components of the single-particle density matrix. The wavefunction of the condensate is an order parameter whose phase is essential in characterizing the coherence and superfluid phenomena. The long-range spatial coherence leads to the existence of phase-locked multiple condensates in an array of superfluid helium, superconducting Josephson junctions or atomic Bose-Einstein condensates. Under certain circumstances, a quantum phase difference of pi is predicted to develop among weakly coupled Josephson junctions. Such a meta-stable pi-state was discovered in a weak link of superfluid 3He, which is characterized by a 'p-wave' order parameter. The possible existence of such a pi-state in weakly coupled atomic Bose-Einstein condensates has also been proposed, but remains undiscovered. Here we report the observation of spontaneous build-up of in-phase ('zero-state') and antiphase ('pi-state') 'superfluid' states in a solid-state system; an array of exciton-polariton condensates connected by weak periodic potential barriers within a semiconductor microcavity. These in-phase and antiphase states reflect the band structure of the one-dimensional polariton array and the dynamic characteristics of metastable exciton-polariton condensates.

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.

In recent years there has been a marked resurgence of interest in the areas of corporate social responsibility (CSR) and social and environmental accounting (SEA) among business, governments, public policymakers, investors, unions, environmentalists and others. While at one level there appears to be widespread agreement that CSR and SEA are worthy topics of attention, different groups have very different understandings of these fields. This article provides an analysis of these differences by comparing three broad approaches to SEA: the business case, stakeholder-accountability and critical theory approaches. It also responds to concerns a number of commentators have expressed regarding the current dominance of 'business case' perspectives. While not seeking to impose on readers a 'correct' way of viewing SEA and CSR, exposure to competing perspectives is viewed as one way of challenging us to think more reflectively about the frames available to us and their implications for the social realities we construct, embed or seek to change.

In a homogeneous two-dimensional system at non-zero temperature there can be no ordering of infinite range 1,2 . However, for a Bose liquid under such conditions, a superfluid phase is predicted 3-5 . Bound vortex-antivortex pairs dominate the thermodynamics and phase coherence properties in this superfluid regime. It is believed that several systems share this behaviour when the parameter describing their ordered state has two degrees of freedom 6 . This theory has been tested for some of them 7-12 , but there has been no direct experimental observation of a quasi-condensate that includes a bound vortex-antivortex pair. Here we present an experimental technique that can identify a single vortex-antivortex pair in a two-dimensional exciton-polariton condensate. The pair is generated through the inhomogeneous spot profile of the pumping laser, and is revealed in the time-integrated phase maps acquired using Michelson interferometry. Numerical modelling based on the open-dissipative Gross-Pitaevskii equation suggests that the pair evolution is distinctly different in this non-equilibrium system compared with atomic condensates 13 .Microcavity exciton polaritons 14 behave as a system of strictly two-dimensional bosons when their density is below the exciton saturation density. As a result of their half-light half-matter nature, their effective mass is extremely small, so that quantum many-body effects are important at relatively high temperatures, even up to room temperature 15 . In particular, dynamic polariton condensation is observed [16][17][18] , and its signatures are similar to Bose-Einstein condensation, namely massive occupation of the ground state and phase coherence up to large distances. However, the short lifetime allows only the formation of a quasi-equilibrium steady state, in which polaritons escaping from the cavity are continuously replenished by the external pump through an intermediate reservoir state.Here, we show that single vortex-antivortex pairs can be observed in an exciton-polariton condensate. We have created a pumping spot that generates a minimum of the condensate density at the centre. A zero in density can be thought of as a superposition of a vortex and antivortex that can be separated by an external perturbation 19 . Thus, the centre of the condensate acts as a source of vortex-antivortex pairs. We have found that for a particular condensate size, there is on average one pair at any time. A Michelson interferometer is used to reconstruct the time-integrated phase map of the system. When the sample disorder potential is stronger than the blueshift induced by polaritonpolariton interactions, pinned pairs appear at certain locations. When the sample disorder potential is weak, on the other hand, they are mobile. They appear along a fixed axis, because of a small asymmetry in the pumping spot, and are created with a random polarization, namely the vortex can appear on the right side of the spot and the antivortex on the left, or vice versa. In the time-integrated measurement, two disti...