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Journal of Experimental and Theoretical Physics Letters

Superradiant Phase Transition in Microstructures with a Complex Network Architecture

A. Yu. Bazhenov, M. M. Nikitina, A. P. Alodjants

Published Jun 1, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.1134/s0021364022600756

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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 ζ≡⟨k2⟩/⟨k⟩\zeta \equiv \langle {{k}^{2}}\rangle {\text{/}}\langle k\rangle ζ≡⟨k2⟩/⟨k⟩ 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.
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.
In the present work we propose a novel quantum material concept, which enables super- 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⟩{\langle}k{\rangle}⟨k⟩, and second normalized, ζ≡⟨k2⟩/⟨k⟩ζ\equiv{\langle}k^2{\rangle}/{\langle}k{\rangle}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⟩{\langle}k{\rangle}⟨k⟩ and ζζζ 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 to design new photonic and polaritonic circuits, quantum networks for efficient processing quantum information at high (room) temperatures.
Abstract One of the long-standing problems in quantum optics and laser physics is the observation of both equilibrium and non-equilibrium (Dicke) superradiant states in two-level (qubit) systems interacting with the quantized electromagnetic (EM) field. We demonstrate that the superradiant phase transition (PT) at thermal equilibrium in such a system is close to ultrastrong light–matter coupling (USC) condition, which is currently available for superconducting devices. We examine the USC regime for EM fields interacting with two-level systems located in highly connected graph nodes of photonic networks beyond the rotating wave approximation. We find that a critical matter–field coupling parameter reduces ⟨ k ⟩ times due to network peculiarities providing suitable conditions for equilibrium PT observation; ⟨ k ⟩ is a network average node degree. We study the non-equilibrium (Dicke) superradiance for the same network system and show that superradiance appears as a non-equilibrium PT to the superradiant laser operating within a bad cavity limit. We show that population inversion in this case plays the same role as the reciprocal temperature inherent to the equilibrium superradiant PT. Our results open new perspectives for experimental observation of superradiance in cavity-free systems in the gigahertz photonic regime and beyond.
In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts for the interaction between a spin-1/2 (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the δ function, random (Poisson), and power-law exponent [p(k)∝k^{-γ}] degree distributions, respectively. To describe paramagnetic (PM)-ferromagrenic (FM) and superradiant (SR) phase transitions we introduce two order parameters: the total weighted spin z component and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in z and x directions, respectively. For the regular networks and vanishing external field we demonstrate that these phase transitions generally represent prerequisites for the crossover from a disordered spin state to the ordered one inherent to the FM and/or SR phase. Due to the interplay between the spin interaction and the finite-size effects in networks we elucidate novel features of the SR state in the presence of the PM-FM phase transition. In particular, we show that the critical temperature may be high enough and essentially depends on parameters which characterize statistical properties of the network structure. For the scale-free networks we demonstrate that the network architecture, characterized by the particular value of γ, plays a key role in the SR phase transition problem. Within the anomalous regime scale-free networks possess a strong effective spin-spin interaction supporting fully ordered FM state, which is practically nonsensitive to variations of the quantum transverse field or moderate classical magnetic field. In a scale-free regime the networks exhibit vanishing of the collective spin component in z direction with increasing γ accompanied by establishing spontaneous magnetization in the transverse field. The SR phase transition occurs in the presence of some FM state. We establish the conditions for the network parameters, classical and quantum field features to obtain a quantum phase transition in the spin system when the critical temperature approaches zero.
Abstract 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.
In this work, we consider an Ising model which allows spin-spin interaction in the systems. We assume that two-level quantum systems are randomly located in N nodes of a complex annealed scale-free network described by the Barabasi-Albert model. It is defined by the power-law degree distribution of nodes. We consider the mean-field approach to the system described by the Ising Hamiltonian. At a certain level, the system is totally characterized by the order parameter Sz. It contains a critical inverse temperature β, which depends on parameter ζ2 as the ratio of the second to the first moment of the degree distribution. We have found that for ζ2, that exceeds its critical value ζ2,c, high temperature phase transition occurs that can be explained by the hubs and clusters which appear in scale-free networks.