Crystalline structures and frustration in a two-component Rydberg gas

TL;DR

This paper explores the complex ground state structures and frustration phenomena in a one-dimensional two-component Rydberg gas, combining analytical and numerical methods to understand classical and quantum regimes.

Contribution

It introduces an analytical and numerical study of frustration and ground state transitions in a two-component Rydberg gas, including an approximation via a Rokhsar-Kivelson Hamiltonian.

Findings

Revealed complex ground state structures with compatible and incompatible phases.

Identified mutual frustration between Rydberg species due to interaction incompatibility.

Developed an analytical approximation explaining frustration effects beyond the classical limit.

Abstract

We study the static behavior of a gas of atoms held in a one-dimensional lattice where two distinct electronically high-lying Rydberg states are simultaneously excited by laser light. We focus on a situation where interactions of van-der-Waals type take place only among atoms that are in the same Rydberg state. We analytically investigate at first the so-called classical limit of vanishing laser driving strength. We show that the system exhibits a surprisingly complex ground state structure with a sequence of compatible to incompatible transitions. The incompatibility between the species leads to mutual frustration, a feature which pertains also in the quantum regime. We perform an analytical and numerical investigation of these features and present an approximative description of the system in terms of a Rokhsar-Kivelson Hamiltonian which permits the analytical understanding of the frustration effects even beyond the classical limit.