One of the most spectacular emergent properties of quantum systems is that of superfluidity. This effect was discovered in 1938 in liquid helium-4 cooled below 2.17K, and is characterised by a set of unusual flow properties, including:

• Dissipationless flow
• No transverse response
• Quantised vortices
• Metastable persistent currents

Notably, such effects are seen in systems that possess long range order, such as Bose-Einstein condesnsates, although quasi-ordered 2D systems can also be superfluids.

Superfluidity has been studied extensively in systems in thermodynamic equilibrium, such as liquid helium or cold atoms. Microcavity-polaritons however, which are quasi-particles formed out of the strong coupling of cavity photons and quantum well excitons, present a different challenge as, due to photons leaking from the cavity, they are out-of-equilibrium and must be pumped to maintain a steady state. Our aim, using a mixture of analytical and computational techniques, is to understand the consequences of this drive and dissipation and thus characterise superfluidity in polaritonic systems.

Polaritons are a good system in which to study superfluidity as their low mass allows them to 'condense' at relatively high temperatures (on the order of 10K in GaAs, but up to room temperature in organic materials), making them relatively accessible experimentally. Such experiments have detected multiple superfluid-like properties in polaritonic systems, although none have demonstrated the full set of flow properties seen in superfluid helium.

For example, in one experiment (Sanvitto et al. Nature Phys. 6 (2010)) a laser pulse was used to create a vortex state in an incoherently pumped system of polaritons, and this state showed the superfluid property of persistence for as long as it could be observed. In another experiment (Berceanu et al. PRB 92 (2015)), this time on coherently pumped polaritons above the OPO (optical parametric oscialltion) threshold where the pump state scatters into two new 'signal' and 'idler' states, the 'signal' state was shown to flow without dissipation past a defect, matching with theoretical predictions.

Coherently pumped polaritons below the OPO threshold present more challenges. Indeed, the phase of the pump state is fixed by the external drive and prevents the formation of vortices. However, it has been shown experimentally and theoretically (Hivet et al. PRB 89 (2014), Cancellieri et al. PRB 90 (2014)) that vortices can form in parts of the system separate from the pump spot, and with the application of a potential can be arranged into lattices. The existence of superfluidity within the pumping area is more contentious however, both due to the aforementioned absence of free vortex formation as well as complications arising from anisotropy and the lack of Galilean invariance that follow from their being a special direction picked out by the pump.