Non-Abelian Thouless pumping in a Rice-Mele ladder

TL;DR

This paper introduces a ladder model demonstrating non-Abelian Thouless pumping, which enables quantum state manipulation and displacement, with potential for experimental realization using cold atoms in optical lattices.

Contribution

It presents a novel ladder model with degenerate bands that exhibits non-Abelian Thouless pumping and connects it to a Yang monopole, advancing quantum control methods.

Findings

Demonstrates non-Abelian Thouless pumping in a ladder model

Shows adiabatic parameter manipulation causes state displacement and geometric transformation

Proposes experimental realization with cold atom optical lattices

Abstract

Non-Abelian Thouless pumping intertwines adiabatic quantum control and topological quantum transport and it holds potential for quantum metrology and computing. In this work, we introduce a ladder model featuring two doubly-degenerate bands and we show that adiabatic manipulation of the lattice parameters results in non-Abelian Thouless pumping, inducing both the displacement of an initially localized state and a geometric unitary transformation within the degenerate subspace. Additionally, we show that the structure and symmetry of the ladder model can be understood through its connection to a Yang monopole model. The proposed Hamiltonian can be realized using cold atoms in optical lattices, enabling the experimental demonstration of non-Abelian Thouless pumping in a genuinely quantum many-body system.