Cooperative Robustness to Static Disorder: Superradiance and localization in a nanoscale ring to model natural light-harvesting systems

We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super and subradiant behavior, an example of cooperative quantum coherent effect. We consider time-independent random fluctuations of the excitation energies. This static disorder, also called inhomogeneous broadening in literature, induces Anderson localization and is able to quench Superradiance. We identify two different regimes: $i)$ weak opening, in which Superradiance is quenched at the same critical disorder at which the states of the closed system localize; $ii)$ strong opening, with a critical disorder strength proportional to both the system size and the degree of opening, displaying robustness of cooperativity to disorder. Relevance to photosynthetic complexes is discussed.