Bulk density signatures of a lattice quasihole with very few particles

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.