Disorder-Induced Exponential Scaling of Subradiant Decay Rates

Abstract

Subradiance, a hallmark cooperative phenomenon in waveguide QED, is characterized by a universal power-law scaling of decay rates with system size and underpins many applications in quantum information storage. Here, we demonstrate that disorder drives a sharp transition in the typical subradiant decay rates from power-law to exponential scaling, a phenomenon we term the subradiant scaling transition (SST). Through rigorous finite-size scaling analysis, we establish the SST as a critical phenomenon, characterized by a diverging characteristic scale of the decay rates at the transition point $W_c=0$. Physically, the SST originates from Anderson localization, manifested by the physical equivalence between the characteristic scale and the localization length of the subradiant states. Our findings provide deep insights into the interplay between disorder and collective dynamics, unifying the underlying physical mechanisms of exponentially-scaled subradiant decay rates and Anderson localization in waveguide QED.