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

Abstract

^{87} Rb 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'}} 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 \Delta and \lambda respectively. We show that when V_{{r r'}} \gg(\ll) \Delta, \lambda for |{r}-{r'}|=1(>1) , these ladders host a plateau for a wide range of \lambda/\Delta 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 \lambda_c/\Delta=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'}|^6 , demonstrate that it survives for a wide range of V_0 , and provide analytic estimate of \lambda_c as a function of V_0 . This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.