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

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 fla...

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Bibliographic Details
Published in:Science bulletin (Beijing) 2021-06, Vol.66 (19)
Main Authors: Zhang, Ren, Lv, Chenwei, Yan, Yangqian, Zhou, Qi
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Discrete scaling symmetry
Efimov-like states
Hyperbolic surfaces
Quantum funneling effects
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Summary: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. Furthermore, 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.
ISSN:2095-9273