Studying the 2D physics utilising a harmonic synthetic dimension; from topologically robust edge-states to how unique interactions effect vortex

标题续：晶格基态我的研究集中在一个谐波合成维，它可以与真实的空间维结合实现新的2D物理。这些尺寸是有效的工具，可用于将人工规范引入各种不同的电荷中性平台，以高度可控的方式模仿磁场对固态系统的影响。对于冷原子平台，其限制陷阱的始终存在的内部谐波态可以耦合以构建一个这样的合成维度。这个特定的合成维度有许多站点，允许访问在合成空间中作用的体物理和独特的远程相互作用。利用谐波合成维数的可调性，我们可以将它与光学晶格或谐波阱中的自由连续维数结合起来，有效地研究有趣的二维物理。在前一种情况下，我们采取紧束缚极限，实质上构建了一个离散的二维晶格，我们研究了涡旋晶格基态以及调和维中的相互作用如何影响它们。晶格的情况下，在伯明翰正在进行的实验合作，我们experimentallseek确定明确的拓扑边缘状态的2D设置。这种状态的鲁棒性，由拓扑不变量保证，对于量子技术的长期应用特别感兴趣-证明了量子模拟领域对这种状态的过多兴趣。总的来说，冷原子平台的可调谐性和合成维度的结合使我们能够获得一系列广泛的物理现象，我们在理论上与实验相结合进行研究。

title continued: lattice ground statesMy research focuses on a harmonic synthetic dimension which can be implemented in combinationwith real space dimensions to realise novel 2D physics. These dimensions are effective tools whichcan be used to induce artificial gauges into various different charge neutral platforms, mimickingeffects magnetic fields have on solid state systems, in a highly controllable way. For cold atomplatforms, the always present, internal harmonic states of their confining traps can be coupled toconstruct one such synthetic dimension. This specific synthetic dimension has many sites allowingaccess to bulk physics and unique long range interactions acting in synthetic space. With thetunability of the harmonic synthetic dimension we can effectively study interesting 2D physics bycombining it with optical lattices or a free continuous dimension inside the harmonic trap. In theformer case, we take the tight-binding limit essentially constructing a discrete 2D lattice wherewe study the vortex lattice ground-states and how the interactions in the harmonic dimensioneffect them. The lattice case, in collaboration with ongoing experiment in Birmingham, we experimentallyseek to identify clear topological edge-states in the 2D set-up. The robustness of suchstates, guaranteed by topological invariants, are particularly of interest for long term applicationto quantum technologies - justifying the plethora of interest in such states in the field of quantumsimulation. Overall, the combination of tunability of cold atom platforms and synthetic dimensionsallows us to access a broad set of physical phenomena which we study theoretically in tandem withexperiment.