A defining property of particles is their behavior under exchange. In twodimensions anyons can exist which, opposed to fermions and bosons, gainarbitrary relative phase factors or even undergo a change of their type. In thelatter case one speaks of non-Abelian anyons - a particularly simple andaesthetic example of which are Fibonacci anyons. They have been studied in thecontext of fractional quantum Hall physics where they occur as quasiparticlesin the $k=3$ Read-Rezayi state, which is conjectured to describe a fractionalquantum Hall state at filling fraction $\nu=12/5$. Here we show that thephysics of interacting Fibonacci anyons can be studied with stronglyinteracting Rydberg atoms in a lattice, when due to the dipole blockade thesimultaneous laser excitation of adjacent atoms is forbidden. The Hilbert spacemaps then directly on the fusion space of Fibonacci anyons and a proper tuningof the laser parameters renders the system into an interacting topologicalliquid of non-Abelian anyons. We discuss the low-energy properties of thissystem and show how to experimentally measure anyonic observables.
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机译：粒子的定义属性是它们在交换下的行为。在二维中，可以存在与费米子和玻色子相反的任意子，它们会获得任意的相对相位因子，甚至经历其类型的变化。在另一种情况下，人们会谈到非阿贝尔的任意韵律-斐波那契任意韵律是一个特别简单的美学示例。在分数量子霍尔物理学的背景下研究了它们，它们以准粒子的形式出现在$ k = 3 $的Read-Rezayi状态下，推测是描述了填充分数$ \ nu = 12/5 $的分数量子霍尔状态。在这里，我们表明，当由于偶极子阻碍而禁止相邻原子同时进行激光激发时，可以用强相互作用的Rydberg原子研究相互作用的斐波那契正午的物理学。然后，希尔伯特空间图直接在斐波那契正午的融合空间上进行，对激光参数的适当调整使系统成为非阿贝尔正午的相互作用的拓扑液体。我们讨论了该系统的低能特性，并展示了如何通过实验测量可测声子。
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