Efimov-like states and quantum funneling effects on synthetic hyperbolic surfaces

人工双曲面上的类Efimov态和量子漏斗效应

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 Poincaréhalf-planes and Poincarédisks,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 Poincaréhalf-plane or its equivalent on the Poincarédisk,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.

具有离散标度不变性的Efimov态吸引了物理学家们长达数十年的兴趣.近年来的研究发现Efimov效应不仅存在于三体问题中,也出现在在拓扑材料、石墨烯等凝聚态物质中.本文指出在双曲平面上的量子态具有跟Efimov态类似的性质.具体来讲,庞加莱半平面和庞加莱圆盘上的非零能本征态是无穷简并的,并且简并态之间存在类似Efimov态的离散标度不变性.因此,作者将这些简并本征态称为类Efimov态.通过操控格点之间的非均匀跃迁强度和格点占据能量,作者指出平直二维空间里的格点模型可以模拟庞加莱半平面、庞加莱盘和其他任意的二维黎曼曲面,并为研究弯曲空间里的新奇量子效应提供了新的平台.例如,双曲空间里存在漏斗口,在双曲坐标系中,系统本征态指数分布在漏斗口附近.因此,在动力学演化过程中,任何初始波包都会朝漏斗口聚集.该现象被称为量子漏斗现象.这是物理学家们首次在厄米系统中发现量子漏斗现象.