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

Abstract

^{87} Rb87Rb atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction V_{{r} {r'}}Vrr′ 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 \DeltaΔ and \lambdaλ respectively. We show that when V_{{r r'}} \gg(\ll) \Delta, \lambdaVrr′≫(≪)Δ,λ for |{r}-{r'}|=1(>1)|r−r′|=1(>1), these ladders host a plateau for a wide range of \lambda/\Deltaλ/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 1/41/4. 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 \lambda_c/\Delta=1/3λc/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 V_{{r} {r'}} = V_0 /|{r}-{r'}|^6Vrr′=V0/|r−r′|6, demonstrate that it survives for a wide range of V_0V0, and provide analytic estimate of \lambda_cλc as a function of V_0V0. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.