Frustrated Rydberg Atom Arrays Meet Cavity-QED: Emergence of the Superradiant Clock Phase

Abstract

Rydberg atom triangular arrays in an optical cavity serve as an ideal platform for understanding the interplay between geometric frustration and quantized photons. Using a large-scale quantum Monte Carlo method, we obtain a rich ground state phase diagram. Around half-filling, the infinite long-range light-matter interaction lifts the ground state degeneracy, resulting in a novel order-coexisted superradiant clock phase that completely destroys the fragile order-by-disorder phase observed in classical light fields. According to the Ginzburg-Landau theory, this replacement may result from the competition between threefold and sixfold clock terms. Similar to the spin supersolid, the clear first-order phase transition at the $Z_2$ symmetry line is attributed to the nonzero photon density, which couples to the threefold clock term. Finally, we discuss the low-energy physics in the dimer language and propose that cavity-mediated nonlocal ring exchange interactions may play a critical role in the rich physics induced by the attachment of cavity-QED. Our work opens a new arena of research on the emergent phenomena of quantum phase transitions in many-body quantum optics.

Figures (22)

• Figure 1: Quantum phase diagrams of Rydberg atom arrays with or without a cavity. Top: The non-cavity phase diagram is obtained from Ref. liuIntrinsicQuantumIsing2020 by transferring the parameters of the TFIM. Bottom: The phase diagram in a cavity is calculated by QMC simulation at $\Delta=9$, where $\tilde{\mu}=\mu_b-3V$. The dashed (solid) lines mark the second (first)-order phase transition. The diamond points represent the two triple points, and the star point labels the 3D XY critical point. The schematic pictures of the OBD phase and SRC phases are pointed with the black arrows.
• Figure 2: (a) Compressibility $\kappa$ and the average total density $\rho_t$; (b) photon density $\rho_a$ and the structure factor $S(\vec{Q})/N$, calculated via QMC simulation at $g=1.8$ and $L=24$.
• Figure 3: (a) Binder cumulant $U_B$ at $\tilde{\mu}=0$ for different system sizes (inset: Rydberg state occupation density), and corresponding (b) finite-size scaling analysis with data collapse. The extracted critical exponent is $1/\nu=1.50\pm0.09$ with phase transition point $g_c=2.440\pm0.00072$. (c-e) Histogram of $s(\vec{Q})$ in the complex plane for different $g$ at $L=24$.
• Figure 4: (a) Structure factor $S(\vec{Q})/N$ and (b) its Binder cumulant $U_B$ calculated by QMC simulation across the SRC-SR transition away from the $Z_2$ symmetry line for $L=24$.
• Figure 5: Dimer representation of ring exchange process in the TFIM, XXZ model, and Rydberg atom array in a cavity.