Observation of a stripe phase in a spin-orbit coupled exciton-polariton Bose-Einstein condensate

In Bose-Einstein condensates, spin-orbit coupling produces supersolidity. It is a peculiar state of matter, which, in addition to the superfluid behaviour of weakly interacting Bose condensates, shows a periodic modulation of its density typical for crystals and called stripe phase. Here, we report the fabrication of a new type of samples allowing to achieve room-temperature supersolidity for a quantum fluid of light. The structure is an optical microcavity filled with a nematic liquid crystal (LC) sandwiched between two layers of the organic polymer MeLPPP. We demonstrate the formation of cavity exciton-polaritons in the presence of Rashba-Dresselhaus spin-orbit coupling (RDSOC), which is tuned by external voltage controlling the LC birefringence. In the RDSOC regime, we demonstrate exciton-polariton condensation in the two distinct degenerate minima of the dispersion. The condensate real space distribution shows both polarization and density stripes, which stem from the interference between phase-coherent condensate components characterized by different wavevectors and polarizations. The possibilities offered by this platform to tune the particle dispersion and to perform full state tomography, including time-resolved, open wide perspectives for detailed future studies of the static and dynamical behaviour of supersolids and of quantum fluids in presence of SOC and topologically non-trivial bands.