Multiparticle interactions for ultracold atoms in optical tweezers: Cyclic ring-exchange terms

TL;DR

This paper proposes a method to implement multi-particle cyclic ring-exchange interactions in optical tweezer arrays with Rydberg atoms, enabling exploration of exotic quantum phases and phase transitions.

Contribution

It introduces a protocol for realizing $SU(N)$ invariant multi-body interactions in optical tweezers, demonstrated through a chiral cyclic ring-exchange Hamiltonian in a ladder geometry.

Findings

Identified phases with vector chirality, ferromagnetism, and Haldane phase via DMRG.

Proposed implementation of frustrated $J-Q$ model for deconfined quantum criticality.

Showed feasibility of engineering complex multi-particle interactions in optical tweezer setups.

Abstract

Dominant multi-particle interactions can give rise to exotic physical phases with anyonic excitations and phase transitions without local order parameters. In spin systems with a global $SU(N)$ symmetry, cyclic ring-exchange couplings constitute the first higher-order interaction in this class. In this letter we propose a protocol how $SU(N)$ invariant multi-body interactions can be implemented in optical tweezer arrays. We utilize the flexibility to re-arrange the tweezer configuration on time scales short compared to the typical lifetimes, in combination with strong non-local Rydberg interactions. As a specific example we demonstrate how a chiral cyclic ring-exchange Hamiltonian can be implemented in a two-leg ladder geometry. We study its phase diagram using DMRG simulations and identify phases with dominant vector chirality, a ferromagnet, and an emergent spin-$1$ Haldane phase. We also discuss how the proposed protocol can be utilized to implement the strongly frustrated $J-Q$ model, a candidate for hosting a deconfined quantum critical point.