Optical Lattice with Torus Topology

TL;DR

This paper proposes an experimental scheme to create an optical lattice with a torus topology, enabling the study of topological quantum states and dynamics in a controlled atomic system.

Contribution

It introduces a novel method to construct a torus-shaped optical lattice using laser beams and high-resolution imaging, facilitating exploration of topological physics.

Findings

Feasibility demonstrated through tunneling strength calculations

Analysis of superfluid currents on the torus

Investigation of FQH state robustness and topological degeneracy

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.