Ising Blockade of Resonant Energy Transport in Dense Spin Ensembles

TL;DR

This paper uncovers an Ising blockade mechanism that explains the slow resonant energy transport in dense spin ensembles, revealing a new scaling law and unifying behaviors across dimensions.

Contribution

It introduces the concept of Ising blockade as a key factor in energy transport, providing a quantitative framework that explains anomalous scaling in spin ensembles.

Findings

Transport is suppressed linearly with Ising broadening, unlike quadratic in traditional models.

A fit-free renormalization relates relaxation time to Ising broadening and experimental linewidth.

The framework unifies 3D and 2D scaling behaviors of relaxation times in spin ensembles.

Abstract

Resonant energy transport in dense, disordered dipolar spin ensembles relaxes far more slowly than predicted by exchange-only theories. We identify the missing mechanism as an Ising blockade: configuration-dependent diagonal interactions dynamically detune neighboring spins, so that the transport bottleneck is set by the correlated pair-detuning $\epsilon_{ij}$ rather than by the single-spin linewidth. The resonant fraction is suppressed linearly with the Ising broadening $\Gamma_{\mathrm{Ising}}$ -- in contrast to the quadratic suppression of conventional relaxation-time approximations. This single emergent scale yields a fit-free renormalization, $T_r^{\mathrm{corr}} \simeq T_r^{\mathrm{orig}}\,\Gamma_{\mathrm{Ising}}/\sigma_{\mathrm{exp}}$, which quantitatively accounts for the anomalous scaling $T_r \propto r^{4.5}$ in three-dimensional superradiant masers. The framework extends naturally across dimensions: geometry-dependent accumulation of Ising fields unifies the 3D exponent with the $T_r\propto r^{3}$ scaling observed in two-dimensional surface spin ensembles.