Polariton lattices: a solid-state platform for quantum simulations of correlated and topological states

The aim of our research in collaboration with three leading experimental groups (in Sheffield, Paris and Berlin) is to explore the recently emerged new solid-state platform, that of polariton lattices, and to optimise it for the holly grails of quantum simulations: quantum-correlated regime and topological protection. The aim of a PhD project in this area will be to develop techniques suitable to study correlated and topological effects in conditions of drive, dissipation and non-equilibrium, directly relevant to those light-matter systems in close collaboration with experimental groups. This could follow one (or more) of the following lines:
1) Adopting stochastic methods, existing in our group, to lattice geometries and calculating correlations within and between lattice sites. These methods will work well in approach to quantum regime but can also be generalised to include quantum corrections, and so to work in the correlated regime.
2) Study correlation between two (or a few) lattice sites using exact quantum optics method (Master equations, quantum jumps and stochastic Schroedinger equations).
3) Analytical methods: mean-field approximation, Keldysh Field theory, Renormalisation Group.
4) Developing Matrix-Product States codes for 1D system including drive and dissipation characteristic for light-matter setting.