Title: Bulk density signatures of a lattice quasihole with very few particles Show Chinese title

Title: 晶格准粒子的体密度特征与少量粒子

Abstract: Motivated by the recent experimental realization of a two-particle fractional quantum Hall state of ultracold atoms in a small optical lattice [Nature 619, 495 (2023)], we propose a minimal setup to create and observe a quasihole in such a system. We find that clear signatures of a quasihole state with two or three atoms can be obtained through a standard site-resolved density measurement provided that the system is appropriately modified with simple additional potential profiles. By adding a single-site repulsive potential to pin the quasihole and superimposing a harmonic trap on top of the optical lattice to keep the particles away from the system edge, we determine via exact diagonalization an optimal range for system parameters such as the magnetic flux and the strengths of the additional potentials that would favour the creation of the quasihole state. We hope that our results will be a useful guide for a possible proof-of-principle experiment that will demonstrate the first controllable creation of a simple quasihole state in a condensed matter system, which will pave the way for the observation of the anyonic statistics of quasiholes in a more complex system. Show Chinese abstract

Abstract: 受最近在小光学晶格中实现两粒子分数量子霍尔态的实验[自然 619, 495 (2023)]的启发，我们提出了一种最小设置来创建和观察这样的系统中的准 Hole。我们发现，通过标准的位点分辨密度测量，可以得到具有两个或三个原子的准 Hole 状态的清晰特征，前提是系统通过简单的附加势场进行了适当的修改。通过添加一个单点排斥势来固定准 Hole，并在光学晶格上叠加一个谐波陷阱以使粒子远离系统边缘，我们通过精确对角化确定了系统参数（如磁通量和附加势的强度）的最优范围，这将有利于准 Hole 状态的创建。我们希望我们的结果将成为可能的原理验证实验的有用指南，该实验将展示在凝聚态系统中首次可控地创建简单准 Hole 状态，这将为在更复杂的系统中观察准 Hole 的任意子统计特性铺平道路。