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

我们与三个领先的实验组（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，极化激元晶格，并优化它的量子模拟的冬青：量子相关制度和拓扑保护。在这一领域的博士项目的目的将是开发适合于研究相关和拓扑效应的驱动，耗散和非平衡的条件下，直接相关的光物质系统与实验组密切合作的技术。这可以遵循以下一条（或多条）路线：1）采用随机方法，现有的在我们的小组，晶格几何形状和计算相关性内和晶格之间的网站。这些方法将很好地工作在量子机制的方法，但也可以推广到包括量子校正，因此在相关机制中工作。用精确量子光学方法计算晶格位置（主方程、量子跃迁和随机薛定谔方程）。3）分析方法：平均场近似，Keldysh场理论，重正化组。4）开发一维系统的矩阵乘积态程序，包括轻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.