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

我们与三个领先的实验小组（在谢菲尔德，巴黎和柏林）合作研究的目的是探索最近出现的新的固态平台，即极化晶格，并为量子模拟的终极目标优化它：量子相关制度和拓扑保护。该领域博士项目的目标是开发适合研究驱动、耗散和非平衡条件下的相关和拓扑效应的技术，与实验组密切合作，直接与这些光物质系统相关。这可以遵循以下一条（或多条）路线：1)采用我们小组中存在的随机方法，以晶格几何形状并计算晶格位置内部和之间的相关性。这些方法可以很好地处理量子状态，但也可以推广到包括量子修正，从而在相关状态下工作。2)利用精确量子光学方法（主方程、量子跃迁和随机薛定谔方程）研究两个（或几个）点阵位之间的相关性。3)分析方法：平均场近似，Keldysh场理论，重整化群。4)开发一维系统的矩阵积态代码，包括光-物质设置的驱动和耗散特性。

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.