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

Abstract

${}^{87}\mathrm{Rb}$ atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction $V_{\mathbf{r}{\mathbf{r}}^{\prime }}$ between excited atoms at sites $\mathbf{r}$ and ${\mathbf{r}}^{\prime }$. Here we study such atoms in a two-leg ladder geometry in the presence of both staggered and uniform detuning with amplitudes $\hat{I}”$ and $\hat{I}»$ respectively. We show that when $V_{\mathbf{r}{\mathbf{r}}^{\prime }}\gg (\ll )\hat{I}”,\hat{I}»$ for $|\mathbf{r}-{\mathbf{r}}^{\prime }|=1(>1)$, these ladders host a plateau for a wide range of $\hat{I}»/\hat{I}”$ 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 $\hat{I}{»}_c/\hat{I}”=1/3$ which agrees well with exact-diagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential $V_{\mathbf{r}{\mathbf{r}}^{\prime }}=V_0/|\mathbf{r}-{\mathbf{r}}^{\prime }{|}^6$, demonstrate that it survives for a wide range of $V_0$, and provide analytic estimate of $\hat{I}{»}_c$ as a function of $V_0$. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.

v2; 22 pages, 9 figs. Minor corrections