Ising-Induced Spectral Broadening Resolves the Relaxation Bottleneck in Superradiant Masers

TL;DR

The paper addresses the slow relaxation observed in self-induced superradiant masers within dense NV center ensembles. It identifies diagonal Ising interactions as the dominant source of inhomogeneous broadening, which detunes resonant flip-flop transport and creates an Ising blockade that suppresses spectral diffusion. By applying Van Vleck’s method of moments to the diamond lattice, the authors quantify the Ising-induced linewidth $\Gamma_{Ising}$ (approximately $43.2\ \mathrm{MHz}$) and show it dwarfs the intrinsic dephasing $\gamma_{\perp}$, thereby renormalizing the effective density of states for transport. This leads to a linear scaling of the relaxation time, $T_r^{corr}=T_r^{orig}(\Gamma_{Ising}/\sigma_{exp})$, yielding $T_r^{corr}\approx13.4\ \mu$s which matches the experimental $\tau_{exp}\approx11.6\ \mu$s without free parameters, establishing diagonal disorder as the governing mechanism for spectral diffusion in dense solid-state spin ensembles.

Abstract

The recent observation of self-induced superradiant masing [[W. Kersten et al., Nat. Phys. 22, 158 (2026)]] revealed a collective relaxation timescale significantly slower than predicted by standard coherent transport models. Here, we elucidate the microscopic origin of this ``relaxation bottleneck.'' We show that in the high-density regime relevant to the experiment, diagonal Ising interactions -- often treated as perturbative -- generate profound inhomogeneous broadening that exceeds the intrinsic single-particle dephasing. This intense diagonal disorder suppresses resonant flip-flop exchange, effectively renormalizing the density of states available for spectral diffusion. Our parameter-free analytic theory quantitatively reproduces the experimentally observed microsecond dynamics, identifying Ising-induced broadening as the governing mechanism for energy transport in dense solid-state spin ensembles.

Figures (1)

• Figure 1: Resolution of the relaxation bottleneck in superradiant masers The relaxation time $T_r$ is plotted against the mean spin separation $r$. The dashed line shows the prediction from standard perturbative transport theory (RTA), which scales as $T_r \propto r^6$ and underestimates the timescale by an order of magnitude. The solid line represents our corrected theory, incorporating Ising-induced inhomogeneous broadening $\Gamma_{\text{Ising}}$. This introduces a dynamic "Ising blockade" that modifies the scaling to $T_r \propto r^3$. The corrected theory quantitatively reproduces the experimental result (circle, from kersten2026) without any free fitting parameters, confirming that diagonal disorder governs the spectral diffusion dynamics.