Quantum phase transitions of the anisotropic Dicke-Ising model in driven Rydberg arrays

TL;DR

The paper tackles the anisotropic Dicke-Ising model realized in driven Rydberg arrays coupled to a cavity, focusing on how the interplay between rotating-wave, counter-rotating-wave, and Ising interactions shapes quantum phase transitions. It introduces a photon-number–aware cluster SSE quantum Monte Carlo method that explicitly tracks the cavity Fock state, enabling finite-size scaling analysis of the superradiant transition and symmetry-breaking phenomena. Key findings include a second-order NP→SR transition and a second-order Solid-1/2→SRS transition, with first-order Solid-1/2→SR and SRS→SR boundaries, largely independent of the anisotropy α, while Rydberg blockade suppresses cavity occupation and CRW terms enhance fluctuations. The work provides detailed theoretical predictions and a practical numerical framework that can be tested in cavity-QED and circuit-QED setups, guiding future experimental and theoretical explorations of light–matter criticality in engineered quantum systems.

Abstract

We study the properties of a generalized Dicke-Ising model realized with an array of Rydberg atoms, driven by microwave electric fields and coupled to an optical cavity. As this platform allows for a precisely tunable anisotropy parameter, the model exhibits a rich landscape of phase transitions and critical phenomena, induced by the interplay of rotating-wave, counter-rotating-wave, and Ising interactions. We develop an improved quantum Monte Carlo algorithm based on the stochastic series expansion that explicitly tracks the Fock state of the quantum cavity. In the superradiant (SR) phase, this allows us to determine, through data collapse, the scaling laws of the photon number. We also demonstrate the vanishing of parity symmetry in finite-size simulations and show that the Rydberg blockade leads to a significant suppression of cavity occupation. Notably, stronger quantum fluctuations induced by the counter-rotating wave terms slightly favor the superradiant solid (SRS) phase over the Solid-1/2 state. Finally, we confirm that the SR phase transition and the transition from the Solid-1/2 to the SRS are second-order. In contrast, the transitions from the Solid-1/2 or SRS to the SR phase are both first-order for any value of the normalized anisotropy parameter.

Figures (8)

• Figure 1: (a) Illustration of the proposed setup, with a two-dimensional Rydberg atom array coupled to an ultrahigh finesse optical cavity and driven by a microwave electric field. (b) Schematic energy-level scheme of a driven Rydberg atom.
• Figure 2: Quantum phase diagram of the AIDM, obtained using the variational state of Eq. (\ref{['VariationalMF']}). All phase boundaries are independent of the NAP $\alpha$. The bottom, middle, and top (red dashed) line cuts are analyzed in Fig. \ref{['phsupress']}, Fig. \ref{['solid']}(c,d), and Fig. \ref{['solid']}(a,b), respectively. The other parameters are $\Delta = 3$ and $V = 1$.
• Figure 3: Possible assignments of the worm head (red solid-line arrow) entering an $H_{cw_{\gamma}^+, j}$ type vertex from the lower left leg (cavity mode state). The numbers in the large polygons indicate the Fock state of the cavity, while black (white) circles represent atoms in the Rydberg (ground) state, the numbers ($\pm 1$) on the arrow head and tail correspond to (add, minus) one of the cavity mode state or flip (up, down) of the atom. The worm head is bounced back with (a) vertex unchanged or (b) cavity mode state increasing two photons and updating to $H_{rw_{\gamma}^+, j}$; continue straight with cavity mode state changed and (c) operator unchanged or (d) updating to $H_{cw_{\gamma}^+, j}$; (e) cross through and (f) turn back with updating to $H_{d_{\gamma}, j}$. The corresponding inverse process is represented by the red dashed arrows.
• Figure 4: Comparison of (a) energy per site and (b) number of excited particles with SSE and ED methods. The parameters of the system are chosen as $\mu = -3.4$, $\Delta = 3$, $\alpha = 0.5$, and $V=1$. Meanwhile, the photon number is truncated to $n_{\mathrm{p}} = 8$ in the ED.
• Figure 5: Dependence of various physical quantities on the coupling strength $g$ around the phase transition point. (a,b) are FSS analysis of $n_{\rm ph}$, and (c, d) present the parity as a function of $g$. Here, the green vertical dashed lines indicate the critical point obtained through FSS, see Table \ref{['ADMcritE']}. The parameters are $\mu = -3.5$ and $\Delta = 3$, with the system sizes $N = 400$ (black triangles), $576$ (red circles), and $784$ (blue crosses), for (a,c) $\alpha=0$ and (b,d) $\alpha=0.5$.