论文标题
EFIMOV样状态和量子漏斗对合成双曲线表面的影响
Efimov-like states and quantum funneling effects on synthetic hyperbolic surfaces
论文作者
论文摘要
具有量身定制的现场隧道和现场能量的工程晶格模型可以用高度可调的局部曲率合成基本任意的riemannian表面。在这里，我们指出，由平面平面的晶格创建的离散合成庞加莱半平台和庞加莱磁盘，为任何非零的特征力均可为无限退化的特征态提供。这种类似Efimov的状态表现出离散的缩放对称性，并暗示了使用双曲线表面研究量子异常的前所未有的设备。此外，所有本征态都在双曲线坐标中呈指数式定位，这表示遗传系统中量子漏斗效应的第一个例子。因此，任何初始波数据包都朝着庞加莱半平面的边缘或在庞加莱磁盘上等效的边缘传播，从而提供了有效的方案，可以在二维中收获光和原子。我们的发现展现了双曲线空间的有趣特性，并表明Efimov状态可以被视为具有额外尺寸的弯曲空间的投影。
Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures. Here, we point out that discrete synthetic Poincaré half-planes and Poincaré disks, which are created by lattices in flat planes, support infinitely degenerate eigenstates for any nonzero eigenenergies. Such Efimov-like states exhibit a discrete scaling symmetry and imply an unprecedented apparatus for studying quantum anomaly using hyperbolic surfaces. Furthermore, all eigenstates are exponentially localized in the hyperbolic coordinates, signifying the first example of quantum funneling effects in Hermitian systems. As such, any initial wave packet travels towards the edge of the Poincaré half-plane or its equivalent on the Poincaré disk, delivering an efficient scheme to harvest light and atoms in two dimensions. Our findings unfold the intriguing properties of hyperbolic spaces and suggest that Efimov states may be regarded as a projection from a curved space with an extra dimension.
