Superradiant phase transition in microstructures with a complex network architecture

A new concept of topological organization of microstructures that maintain the ultrastrong coupling of two-level systems to a photon field and have the topology of a network (graph) with a power-law node degree distribution has been proposed. A phase transition to the superradiant state, which leads to the formation of two dispersion branches of polaritons and is accompanied by the appearance of a nonzero macroscopic polarization of two-level systems, has been studied within the mean field theory. It has been found that the specific behavior of such a system depends on the statistical characteristics of the network structure, more precisely, on the normalized second moment $\zeta\equiv{\langle}k^2{\rangle}/{\langle}k{\rangle}$ of the distribution of node degrees. It has been shown that the Rabi frequency can be significantly increased in the anomalous regime of the network structure, where $\zeta$ increases significantly. The multimode (waveguide) structure of the interaction between matter and field in this regime can establish a ultrastrong coupling, which is primarily responsible for the high-temperature phase transition.