Quantum spin liquid state of a dual-species atomic array on Kagome lattice

Dual-species arrays of ultracold neutral atoms have recently attracted increased interest due to the ability to independently control different atomic species and tune the interatomic interactions. This capability provides additional flexibility essential for both quantum computing and quantum simulation. In this work we theoretically investigate a quantum spin liquid (QSL) state to be simulated on a programmable quantum simulator based on a dual-species atomic array, arranged on a Kagome lattice. The Kagome lattice is formed by corner sharing triangles. This specific spatial arrangement enhances the competing interactions between atoms and is often considered as a model for realizing QSL states. When the atoms are excited into Rydberg states, long-range interactions result in Rydberg blockade. The geometric frustration of the Kagome lattice, combined with the Rydberg blockade, drives the system into exotic phases with topological order and long-range entanglement. To drive an array into the QSL state, we use a sweep-hold-sweep protocol, when the atoms are quasi-adiabatically excited into Rydberg state with individually controlled detuning from the resonance for each atomic species. The filling fraction, indicating emergence of a QSL state, is represented by a density of Rydberg excitations. We identified the conditions required for QSL state in a dual-species array with non-uniform interaction energies. We calculated the correlation length and studied the mutual information as a function of the size of the subset of the system. The existence of a topological order was proved by estimating the Kitaev-Preskill topological quantum entanglement entropy, and further confirmed by evaluating diagonal and off-diagonal topological string operators, which respectively probe the classical dimer-covering structure and the quantum coherence between distinct dimer configurations.