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

^87 Rb 87 R b atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction Vₑ {r'} V r r ′ between excited atoms at sites r r and r' r ′. Here we study such atoms in a two-leg ladder geometry in the presence of both staggered and uniform detuning with amplitudes Δ and λ respectively. We show that when Vₑ ₑ' (), V r r ′ ≫ (≪) Δ, λ for |r-r'|=1 (1) | r − r ′ | = 1 (> 1), these ladders host a plateau for a wide range of / λ / Δ 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 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 c/=1/3 λ c / Δ = 1 / 3 which agrees well with exact-diagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential Vₑ {r'} = V₀ /|r-r'|⁶ V r r ′ = V 0