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

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.

arXiv comment7 pages, 4 figures

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Cited by in corpus (4)

• Laughlin's topological charge pump in an atomic Hall cylinder
• Realization of an atomic quantum Hall system in four dimensions
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems