In the present work we propose a novel, to the best of our knowledge, quantum material concept, which enables superstrong and/or ultrastrong interaction of two-level systems with the photonic field in a complex network. Within the mean field approximation we examine phase transition to superradiance that results in two excitation (polariton) branches and is accompanied by the appearance of non-zero macroscopic polarization of two-level systems. We characterize the statistical properties of networks by the first, 〈k〉, and second normalized, ζ ≡ 〈k2〉/〈k〉, moments for node degree distribution. We have shown that the Rabi frequency is essentially enhanced due to the topology of the network within the anomalous domain where 〈k〉 and ζ sufficiently grow. The multichannel (multimode) structure of matter–field interaction leads superstrong coupling that provides primary behavior of the high temperature phase transition. The results obtained pave the way for the design of new photonic and polaritonic circuits, quantum networks for efficient processing quantum information at high (room) temperatures.

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 $$\zeta \equiv \langle {{k}^{2}}\rangle {\text{/}}\langle k\rangle $$ 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 ζ 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.

An Erratum to this paper has been published: https://doi.org/10.1134/S0021364022380027

In this work we examine a superradiant (SR) and/or ferromagnetic (FM) - paramagnetic (PM) phase transitions problem in quantum materials which may be established by Barabási-Albert (BA) scale-free network that possesses power law degree distribution and specific degree correlations. We represent quantum material by means of Dicke-Ising model, that describes the interaction between a spin-1/2 (two-level) system and external classical (magnetic) and quantized (transverse) fields. To describe PM-FM and SR phase transitions we introduce three order parameters: the total (topologically) weighted as well as un-weighted z-spin components, and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in z- and x-directions, respectively. We have shown that SR state occurs as a result of the interaction between the ordering of the spins in the z− and x-directions and depends on assortativity or disassortativity of the network medium. We have shown that non-trivial topological behavior associated with large fluctuations of network parameters inherent to assortative networks reduces of PM-FM phase transition temperature, while dissasortative networks exhibit high temperature phase transitions. Our findings demonstrate new opportunities to design of quantum materials which may be implemented for current quantum technologies at relatively high temperatures.

The theory of a random laser with an interface in the form of random or scale-free networks whose nodes are occupied by microcavities with quantum two-level systems has been proposed for the first time. The microcavities are coupled to each other through light-guiding channels forming edges of the network. It has been shown that such a laser has a number of spectral features associated with the statistical properties of the network structure. Among them are the existence of a topologically protected Perron eigenvalue caused by the presence of a strong mean field at the node of maximum influence located in the central part of the network and the delocalization/localization of radiation modes depending on the probability of coupling between arbitrary microcavities. The results obtained in this work open prospects for the fabrication of new low-threshold laser sources.