Semiconductor microcavities are used to support freely flowing polariton quantum liquids allowing the direct observation and optical manipulation of macroscopic quantum states. Incoherent optical excitation at a point produces radially expanding condensate clouds within the planar geometry. By using arbitrary configurations of multiple pump spots, we discover a geometrically controlled phase transition, switching from the coherent phase-locking of multiple condensates to the formation of a single trapped condensate. The condensation threshold becomes strongly dependent on the programmed superfluid geometry and sensitive to cooperative interactions between condensates. We directly image persistently circulating superfluid and show how flows of light-matter quasiparticles are dominated by the quantum pressure in such configurable laser-written potential landscapes.

Exciton-polariton condensates display a variety of intriguing pattern-forming behaviors, particularly when confined in potential traps. It has previously been predicted that triangular lattices of vortices of the same sign will form spontaneously as the result of surface instabilities in a harmonic trap. However, natural disorder, deviation of the external potential from circular symmetry, or higher-order terms modifying the dynamical equations may all have detrimental effects and destabilize the circular trajectories of vortices. Here we address these issues by characterizing the robustness of the vortex lattice against disorder and deformations of the trapping potential. Since most experiments use time-integrated measurements, it would be hard to observe directly the rotating vortex lattices or distinguish them from vortex-free states. We suggest how these difficulties can be overcome and present an experimentally viable interference-imaging scheme that would allow the detection of rotating vortex lattices.

Abstract:We analyse the properties of a (4+1)-dimensional Ricci-flat spacetime which may be viewed as an evolving Taub-NUT geometry, and give exact solutions of the Maxwell and gauged Dirac equation on this background. We interpret these solutions in terms of a geometric model of the electron and its spin, and discuss links between the resulting picture and Dirac's Large Number Hypothesis.

This paper studies the space of L 2 harmonic forms and L 2 harmonic spinors on Taubbolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find all L 2 zero modes of / D A , the Dirac operator twisted by an arbitrary L 2 harmonic connection A, and independently compute the index of / D A . We compare our results with those known in the case of Taub-NUT and Euclidean Schwarzschild as these manifolds present interesting similarities with Taub-bolt. In doing so, we generalise known results concerning harmonic spinors on Euclidean Schwarzschild.