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

arXiv commentv2; 22 pages, 9 figs. Minor corrections

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• Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians
• Emergence of a quasi-ergodic steady state in a dissipative Tavis-Cummings array
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders
• Scar-induced imbalance in staggered Rydberg ladders
• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
• Phase diagram of Rydberg atoms in a two-leg rectangular ladder
• Quantum dynamics of a spin model with an extensive degeneracy
• Rydberg Atoms in a Ladder Geometry: Quench Dynamics and Floquet Engineering