  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.
