Synthetic Helical Liquids with Ultracold Atoms in Optical Lattices

Abstract

We discuss a platform for the synthetic realization of key physical properties of helical Tomonaga Luttinger liquids (HTLLs) with ultracold fermionic atoms in one-dimensional optical lattices. The HTLL is a strongly correlated metallic state where spin polarization and propagation direction of the itinerant particles are locked to each other. We propose an unconventional one-dimensional Fermi-Hubbard model which, at quarter filling, resembles the HTLL in the long wavelength limit, as we demonstrate with a combination of analytical (bosonization) and numerical (density matrix renormalization group) methods. An experimentally feasible scheme is provided for the realization of this model with ultracold fermionic atoms in optical lattices. Finally, we discuss how the robustness of the HTLL against back-scattering and imperfections, well known from its realization at the edge of two-dimensional topological insulators, is reflected in the synthetic one-dimensional scenario proposed here.

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Cited by in corpus (11)

• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Synthetic gauge fields in synthetic dimensions: Interactions and chiral edge modes
• Floquet chiral magnetic effect
• Helical Floquet Channels in 1D Lattices
• Synthetic dimensions in the strong-coupling limit: supersolids and pair-superfluids
• Majorana Quasi-Particles Protected by ${\mathbb{Z}}_2$ Angular Momentum Conservation
• Synthesizing Majorana zero-energy modes in a periodically gated quantum wire
• Helical transport in coupled resonator waveguides
• Spin-gap spectroscopy in a bosonic flux ladder
• Operator correlations in a quenched non-Hermitian Luttinger liquid
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains