Superradiant phase transition in complex networks

Abstract

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 the interaction between a spin (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the delta-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. Due to the interplay between the spin interaction and the finite size effects in the networks we first elucidate novel features of the SR state in the presence of the PM-FM phase transition. In particular, we show that the critical temperature essentially depends on parameter ζ = k 2 / k , which characterizes statistical properties of the network structure. Moreover, we reveal that the critical temperature of the SR phase transition grows monotonically from some certain value that corresponds to the critical number of nodes. For the scale-free networks we find that this critical temperature rises with the degree exponent increase accompanied both by establishing spontaneous magnetization in a quantum transverse field and vanishing of the collective spin component in z direction. In addition, we establish the conditions for the network parameters to obtain a quantum phase transition in the spin system when the critical temperature approaches zero. The fundamental features, which involve critical values of the classical and quantum field parameters, are discussed for the occurrence of the superradiance phase in this limit.

The Jaynes-Cummings model and its descendants

“…In [920] the atomic motion is quantized taking into account quantum fluctuations. A simplification could be to consider the atoms as point-like fixed points, but spatially distributed in the cavity such that the coupling strength becomes g → g i with g i a random variable with the subscript i marking atom i [921,922]. It was found that this modification could lead to a series of new transitions between ground states with abrupt changes in their atom-field entanglement.…”