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

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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.