Prethermalization of light and matter in cavity-coupled Rydberg arrays

TL;DR

This work analyzes how a two-dimensional Rydberg-atom array embedded in a single-mode cavity exhibits prethermalization due to competing short-range and photon-mediated long-range interactions. Using nonequilibrium 2PI Keldysh techniques with a Majorana representation and a controlled $1/N$/$1/N_s$ expansion, the authors track light–matter correlations and define separate effective temperatures for photons and spins. They identify regimes where light and matter equilibrate at distinct, including negative, temperatures, revealing metastable states and slow approaches to global thermalization. The results demonstrate that strongly correlated AMO platforms are powerful for exploring quantum thermalization in higher dimensions and offer tunable knobs for probing fundamental questions in non-equilibrium statistical mechanics.

Abstract

We explore the dynamics of two-dimensional Rydberg atom arrays coupled to a single-mode optical cavity, employing nonequilibrium diagrammatic techniques to capture nonlinearities and fluctuations beyond mean-field theory. We discover a novel prethermalization regime driven by the interplay between short-range Rydberg interactions and long-range photon-mediated interactions. In this regime, matter and light equilibrate at distinct - and in some cases opposite - effective temperatures, resembling the original concept of prethermalization from particle physics. Our results establish strongly correlated AMO platforms as tools to investigate fundamental questions in statistical mechanics, including quantum thermalization in higher-dimensional systems.

Figures (5)

• Figure 1: (a) A two-dimensional Rydberg atomic array in a single-mode optical cavity. Rydberg interactions $\lambda$ induce anti-ferromagnetism between spins on neighboring sites, which competes against the long-range photon-mediated interaction of strength $g$. Photons leak from the cavity at rate $\kappa$. (b) Cartoon of the dynamical phase diagram. When photon-mediated long-range interaction plays the dominant role, the model displays fast thermalization, with matter and light quickly reaching the same temperature. In the opposite regime, light and matter prethermalize at different temperatures, featuring regimes where the atoms can stay trapped in a metastable state characterized by a negative effective temperature.
• Figure 2: (a) Time dependence of the spin and photon effective temperatures. The parameters are taken as $(\Delta,\lambda) = (-0.1,0.5)$ and $g = 0.5, 0.25$, and $0.15$ for regimes I, II, and III, respectively. The semitransparent ribbons represent the uncertainty arising from averaging $T_{\mathrm{eff}}$ over small frequency and time windows according to the procedure detailed in SM. Initially large, temperature deviations gradually vanish, signaling a transition to the regime where the notion of effective temperatures becomes reliable. (b) Spin and photon effective time temperatures taken at time $\tau=140$, and displayed as a function of the Dicke coupling $g$ (we mark this time in panel (a) by the vertical black dashed line). The gray vertical lines indicate the values of $g$ used in the respective regimes in (a).
• Figure 3: Plots of observables for the same initial conditions and values of coupling constants as in Fig. \ref{['fig:Ts_ph']}. (a) Time dependence of the photon coherence (top) and of the staggered magnetization (bottom). Gray dashed lines mark the onset of (pre)thermalization as extracted from Fig. \ref{['fig:Ts_ph']}. (b) Photon (top) and spin (bottom) spectral functions at time $\tau=140$ across the three dynamical regimes. In regime III, the spin spectral function is inverted at low frequencies, signaling a negative effective temperature.
• Figure S1: (a) Absolute values of the "occupation numbers" $n$ at $\tau = 140$ for photon and spin degrees of freedom, respectively. The shaded areas represent the frequency windows $(\omega_{\mathrm{min}},\omega_{\mathrm{max}})$ taken in Eq. \ref{['eq:T_average']} for the respective degree of freedom. For consistency, we use the same frequency windows for all the parametric regimes considered in this work. We note that, since the definition of $n$ involves the quotient of $F$ and $\rho$, cf. Eq. \ref{['eq:FDR']} and the subsequent discussion, the high-frequency region, where the value of $\rho$ drops below the numerical tolerance, suffers from the numerical artifacts and is thus not shown here. (b) Effective spin temperatures extracted from the local correlation functions on each sublattice. The two sublattices quickly thermalize with each other, exhibiting no qualitative difference throughout the entire dynamics.
• Figure S2: Number of photons per spin for the three parametric regimes discussed in the main text.