Some remarks on ‘superradiant’ phase transitions in light-matter systems

Abstract

Abstract.In this paper we analyze properties of the phase transition that appears in a set of quantum optical models; Dicke, Tavis-Cummings, quantum Rabi, and finally the Jaynes-Cummings model. As the light-matter coupling is increased into the deep strong coupling regime, the ground state turns from vacuum to become a superradiant state characterized by both atomic and photonic excitations. It is pointed out that all four transitions are of the mean-field type, that quantum fluctuations are negligible, and hence these fluctuations cannot be responsible for the corresponding vacuum instability. In this respect, these are not quantum phase transitions. In the case of the Tavis-Cummings and Jaynes-Cummings models, the continuous symmetry of these models implies that quantum fluctuations are not only negligible, but strictly zero. However, all models possess a non-analyticity in the ground state in agreement with a continuous quantum phase transition. As such, it is a matter of taste whether the transitions should be termed quantum or not. In addition, we also consider the modifications of the transitions when photon losses are present. For the Dicke and Rabi models these non-equilibrium steady states remain critical, while the criticality for the open Tavis-Cummings and Jaynes-Cummings models is completely lost, i.e. in realistic settings one cannot expect a true critical behaviour for the two last models.

Introduction to the Dicke Model: From Equilibrium to Nonequilibrium, and Vice Versa

“…In the presence of decay, the Tavis-Cummings model does not show a superradiant transition. [21,113,114] This result has a simple physical meaning: because the model does not have counterrotating terms, it will always flow to a trivial steady state, where the cavity is empty and the spins are polarized in the σ z = −1/2 direction. The superradiant transition occurs only if the total number of excitations is kept constant (when no loss processes are present).…”

Quantum criticality and state engineering in the simulated anisotropic quantum Rabi model

“…Actually, the experimental verification of this anisotropic involved universality is urgently needed. Being different from typical physical quantities whose features have already been investigated in the AQRM [10,25,31,32], here for finite frequency ratio, we design a cumulant ratio as which can be considered as an analogy to the famous Binder cumulant ratio of the dimensional criticality in a statistical system [61,62]. The cumulant ratio U X , which needs to measure the quadrature of the displacement, may possibly be performed with squeezed quadrature quantum tomography of the electro-magnetic field using homodyne or heterodyne detection [63,64] and together with photon number measurement [16].…”

“…The studies in [25] show that the AQRM with any finite values of l 1 0 belongs to the same universality class as the QRM, but the special case of l = 0 for the JCM belongs to a different universality class [31]. It is also worth mentioning that, due to the negligible quantum fluctuations, it is still a debate whether the zero-temperature superradiant phase transition in the AQRM can be understood as a QPT or not [32]. With the simulated AQRM, i.e.,equation (5) in hand, the free adjustment of parameters allows us to investigate many interesting issues like the critical phenomena and the universal properties.…”

“…QPT in systems with few degrees of freedom has recently been a topic of major interest recently [10,25,31,32,45]. Although the quantum criticality is commonly believed to take place in a many-body system in the thermodynamic limit, it is newly realized that a few-body system may undergo QPTs provided the energy barrier between two local-minima states is infinite.…”

“…It is a generalization of the QRM affiliated with l denoting the asymmetry between rotating and 0 [26], or the original QRM with l = 1. Since individual addressing of the two coupling constants are allowed, the AQRM presents a favorable test bed for many valuable theoretical issues, such as the role of the counter-rotating terms [27][28][29], the Fisher information [30], the universality scaling of quantum phase transition (QPT) [10,25,31,32], the enhanced squeezing [24], and thus it may bridge the gap between the JCM and the QRM in the dynamics [33]. The discussions of the anisotropy in the standard AQRM were further extended to the semi-classical case [34], the multi-qubit case [25,35] (namely the anisotropic Dicke model).…”