Simulating two-dimensional dynamics within a large-size atomic spin

TL;DR

This paper introduces a method to encode two-dimensional synthetic spaces within a large atomic spin, enabling advanced quantum simulations of topological and high-dimensional geometries using lanthanide atoms.

Contribution

It extends the synthetic dimension approach by combining spin couplings to encode two dimensions in a large atomic spin, suitable for lanthanide atoms.

Findings

Proposes a protocol encoding two dimensions in a large atomic spin.

Suitable for simulating topological systems with periodic boundary conditions.

Applicable to lanthanide atoms with large electronic spins.

Abstract

Encoding a dimension in the internal degree of freedom of an atom provides an interesting tool for quantum simulation, facilitating the realization of artificial gauge fields. We propose an extension of the synthetic dimension toolbox, making it possible to encode two dimensions within a large atomic spin. The protocol combines first- and second-order spin couplings, such that the spin projection $m$ and the remainder $r=m$ (mod 3) of its Euclidian division by 3 act as orthogonal coordinates on a synthetic cylinder. It is suited for an implementation with lanthanide atoms, which feature a large electronic spin and narrow optical transitions for applying the required spin couplings. This method is useful for simulating geometries with periodic boundary conditions, and engineering various types of topological systems evolving in high dimensions.