Emergent periodic and quasiperiodic lattices on surfaces of synthetic Hall tori and synthetic Hall cylinders

TL;DR

This paper demonstrates how synthetic spaces, specifically Hall tori and cylinders created with ultracold atoms and Laguerre-Gaussian beams, can produce novel periodic and quasiperiodic lattice structures with unique quantum properties.

Contribution

It introduces a method to realize synthetic Hall tori and cylinders with effective magnetic flux, leading to fractional density modulations, multiple energy bands, and protected band crossings.

Findings

Fractional density modulation in synthetic Hall lattices

Multiple energy bands with nonsymmorphic symmetry

Wavepacket braiding in Bloch oscillations

Abstract

Synthetic spaces allow physicists to bypass constraints imposed by certain physical laws in experiments. Here, we show that a synthetic torus, which consists of a ring trap in the real space and internal states of ultracold atoms cyclically coupled by Laguerre-Gaussian Raman beams, could be threaded by a net effective magnetic flux through its surface---an impossible mission in the real space. Such synthetic Hall torus gives rise to a periodic lattice in the real dimension, in which the periodicity of density modulation of atoms fractionalizes that of the Hamiltonian. Correspondingly, the energy spectrum is featured by multiple bands grouping into clusters with nonsymmorphic symmetry protected band crossings in each cluster, leading to braidings of wavepackets in Bloch oscillations. Our scheme allows physicists to glue two synthetic Hall tori such that localization may emerge in a quasicrystalline lattice. If the Laguerre-Gaussian Raman beams and ring traps were replaced by linear Raman beams and ordinary traps, a synthetic Hall cylinder could be realized and deliver many of the aforementioned phenomena.