Optical Lattice with Torus Topology

Abstract

We propose an experimental scheme to construct an optical lattice where the atoms are confined to the surface of a torus. This construction can be realized with spatially shaped laser beams which could be realized with recently developed high resolution imaging techniques. We numerically study the feasibility of this proposal by calculating the tunneling strengths for atoms in the torus lattice. To illustrate the non-trivial role of topology in atomic dynamics on the torus, we study the quantized superfluid currents and fractional quantum Hall (FQH) states on such a structure. For FQH states, we numerically investigate the robustness of the topological degeneracy and propose an experimental way to detect such a degeneracy. Our scheme for torus construction can be generalized to Riemann surfaces with higher genus for exploration of richer topological physics.

arXiv comment5+8 pages, 4+5 figures

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Cited by in corpus (13)

• Many-body Chern number from statistical correlations of randomized measurements
• Theoretical Prediction of Non-Hermitian Skin Effect in Ultracold Atom Systems
• Bose-Einstein Condensate on a Synthetic Topological Hall Cylinder
• Emergent periodic and quasiperiodic lattices on surfaces of synthetic Hall tori and synthetic Hall cylinders
• Real-space probe for lattice quasiholes
• Two-Dimensional Thouless Pumping of Ultracold Fermions in Obliquely Introduced Optical Superlattice
• Vortex Pairs in the Discrete Nonlinear Schrödinger Equation
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
• Protocol for nonlinear state discrimination in rotating condensate
• Superfluid vortex multipoles and soliton stripes on a torus
• Localization and persistent currents in a quasiperiodic disordered helical lattice
• Quantum States and Spectra of Small Cylindrical and Toroidal Lattices