Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning

Abstract

87Rb atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction Vrr′ between excited atoms at sites r and r′. Here we study such atoms in a two-leg ladder geometry in the presence of both staggered and uniform detuning with amplitudes ∆ and λ respectively. We show that when Vrr′ ≫ (≪)∆, λ for |r − r′| = 1(> 1), these ladders host a plateau for a wide range of λ/∆ where the ground states are selected by a quantum order-by-disorder mechanism from a macroscopically degenerate manifold of Fock states with fixed Rydberg excitation density 1/4. Our study further unravels the presence of an emergent Ising transition stabilized via the order-by-disorder mechanism inside the plateau. We identify the competing terms responsible for the transition and estimate a critical detuning λc/∆ = 1/3 which agrees well with exact-diagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential Vrr′ = V0/|r−r′|6, demonstrate that it survives for a wide range of V0, and provide analytic estimate of λc as a function of V0. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.