Spinor superfluid currents of exciton-polaritons on a split-ring

Recently, split-ring bosonic condensates of exciton polaritons have been proposed for realisation of qubits. We formulate an analytical model of a polariton condensate in a one-dimensional ring split by a delta-function potential. The persistent current is stopped by the potential defect embedded in a scalar condensate of non-interacting particles, however, it reappears in the presence of an up-critical non-linearity. The nonlinear supercurrents are characterised by fractional orbital momenta while their eigenfunctions may feature grey or dark solitons. The coupling between the spin and the orbital angular momentum of a spinor condensate affects persistent currents crucially. We show that the spin-orbit interaction (SOI) induces the net superfluid current in the condensate with a spatially uniform spin polarisation. We also find solutions where the SOI-induced currents of two spin components of the condensate propagate in opposite directions. The corresponding states of spinor condensates obey a combined mirror reflection and the spin-flip symmetry.