Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter. On a lattice, gauge invariance and gauge-invariant (plaquette) interactions involve (at least) four-body interactions that are challenging to realize. Here, we show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian—a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics. Using an electromagnetic duality, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade. Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs. We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically and probe them and their quench dynamics by on-site measurements of their quantum correlations. We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.

中文翻译：

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Rydberg可配置阵列中的新兴二维量规理论

在从高能物理到凝聚态的几个物理领域中，解决二维或三个空间维中的强耦合规范理论至关重要。在晶格上，规范不变性和规范不变（样板）相互作用涉及（至少）四体相互作用，这些相互作用很难实现。在这里，我们证明了在当前的镊子实验中实现的可配置阵列中的Rydberg原子是实现Rokhsar-Kivelson哈密顿量的可扩展模拟器的自然平台-一种描述量子二聚体和自旋冰动力学的二维U（1）晶格规理论。使用电磁对偶，我们将板块相互作用实现为受Rydberg封锁的Rabi振荡。值得注意的是 我们表明，通过控制阵列中的原子排列，我们可以为由原子对构成的自旋设计各向异性相互作用和广义的封锁条件。我们描述了如何绝热地制备Rokhsar-Kivelson哈密顿量的共振价键和晶相，并通过现场测量它们的量子相关性来探测它们以及它们的猝灭动力学。我们讨论了Rydberg模拟器在晶格规理论和奇异自旋模型上的潜在应用。