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arXiv:2502.10839 · Physical Review A

Quantum phase transitions in a Dicke trimer with both photon and atom hoppings

Jun-Wen Luo, Bo Wang, Ze-Liang Xiang

Published Feb 23, 2026• 3 citations
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Abstract

We investigate superradiant quantum phase transitions in a Dicke trimer model consisting of two types of hoppings, i.e., photon hoppings and atom hoppings. In the superradiant regime, the system can exist in two distinct phases: normal and frustrated superradiant phases, which are governed by both types of hoppings. Particularly, the interplay between these hoppings gives rise to interesting effects, such as triggering superradiance with much lower coupling strengths when both hoppings exhibit the same tendency. In contrast, with opposite tendencies, the competition between hoppings leads to a first-order phase transition between two different superradiant phases with translational symmetry broken. These findings enable the system to undergo a sequence of transitions across three phases by changing the coupling strength. Our work provides deep insights into competing interactions and quantum phase transitions in multi-cavity systems with geometric structures.

DOI
10.1103/ywj2-hm54

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We investigate superradiant quantum phase transitions in a Dicke trimer model consisting of two types of hoppings, i.e., photon hoppings and atom hoppings. In the superradiant regime, the system can exist in two distinct phases: normal and frustrated superradiant phases, which are governed by both types of hoppings. Particularly, the interplay between these hoppings gives rise to interesting effects, such as triggering superradiance with much lower coupling strengths when both hoppings exhibit the same tendency. In contrast, with opposite tendencies, the competition between hoppings leads to a first-order phase transition between two different superradiant phases with translational symmetry broken. These findings enable the system to undergo a sequence of transitions across three phases by changing the coupling strength. Our work provides deep insights into competing interactions and quantum phase transitions in multi-cavity systems with geometric structures.
Frustration occurs when a system cannot find a lowest-energy configuration due to conflicting constraints. We show that a frustrated superradiant phase transition occurs when the ground-state superradiance of cavity fields due to local light-matter interactions cannot simultaneously minimize the positive photon hopping energies. We solve the Dicke trimer model on a triangle motif with both negative and positive hopping energies and show that the latter results in a sixfold degenerate ground-state manifold in which the translational symmetry is spontaneously broken. In the frustrated superradiant phase, we find that two sets of diverging time and fluctuation scales coexist, one governed by the mean-field critical exponent and another by a novel critical exponent. The latter is associated with the fluctuation in the difference of local order parameters and gives rise to site-dependent photon number critical exponents, which may serve as an experimental probe for the frustrated superradiant phase. We provide a qualitative explanation for the emergence of unconventional critical scalings and demonstrate that they are generic properties of the frustrated superradiant phase at the hand of a one-dimensional Dicke lattice with an odd number of sites. The mechanism for the frustrated superradiant phase transition discovered here applies to any lattice geometries where the antiferromagnetic ordering of neighboring sites are incompatible and therefore our work paves the way toward the exploration of frustrated phases of coupled light and matter.
Superradiant phase transitions play a fundamental role in understanding the mechanism of collective light–matter interaction at the quantum level. Here we investigate multiple superradiant phases and phase transitions with different symmetry-breaking patterns in a two-mode V-type Dicke model. Interestingly, we show that there exists a quadruple point where one normal phase, one global symmetry-breaking superradiant phase, and two local symmetry-breaking superradiant phases meet. Such a global phase results from the phase competition between two local superradiant phases and cannot occur in the standard Λ- and Ξ-type three-level configurations in quantum optics. Moreover, we exhibit a sequential first-order quantum phase transition from one local to the global again to the other local superradiant phase. Our study opens up a perspective of exploring multilevel quantum critical phenomena with global symmetry breaking.
We investigate the emergence of frustrated quantum phases in a Jaynes-Cummings (JC) trimer with complex hopping amplitudes between the cavities, which represents the smallest frustrated unit in light-matter systems. The complex hopping amplitudes that can be engineered via synthetic gauge fields introduce chiral effects and geometric frustration into the system.We obtain analytic solutions in the semiclassical limit and map out the phase diagram of this model, featuring one normal and three distinct superradiant phases. Among these phases, a chirally frustrated superradiant phase emerges, characterized by broken chiral and translational symmetries and unidirectional photon flow. These results reveal how frustration and symmetry breaking can arise in JC systems with synthetic gauge fields and ultrastrong coupling.
We study the nonequilibrium steady states of an open anisotropic quantum Rabi trimer. Combining semiclassical and quantum mechanical treatments, we map out the system's phase diagram and elucidate the critical phenomena induced by anisotropic light-matter coupling, cavity dissipation, and complex photon hopping, which give rise to abundant multistable phases. Counterintuitively, the frustrated superradiant phase (FSP) can be stabilized by both positive and negative photon hopping, a feature absent in closed Rabi and Dicke trimers. We further uncover two independent dissipation thresholds for the normal superradiant phase and the FSP. Unlike isotropic open quantum Rabi trimers, both phases are suppressed once the dissipation exceeds their respective critical values. The rotating and counter-rotating interaction terms exhibit mutually reciprocal effects on the quantum phase transitions. By analyzing universal scaling behaviors with quantum fluctuations incorporated, we reveal an unprecedented finite-fluctuation critical exponent for the FSP. Moreover, the critical exponents of individual phases are coupling-strength dependent. The multistability and FSP can be tuned by anisotropy and dissipation. Our results broaden the scope of nonequilibrium quantum phase physics in few-body systems and hold promising applications for quantum state engineering and cavity/circuit quantum electrodynamics.
Abstract In this article, we use the spin coherent state transformation and the ground state variational method to theoretically calculate the ground function. In order to consider the influence of the atom-atom interaction on the extended Dicke model’s ground state properties, the mean photon number, the scaled atomic population and the average ground energy are displayed. Using the self-consistent field theory to solve the atom-atom interaction, we discover the system undergoes a first-order quantum phase transition from the normal phase to the superradiant phase, but a famous Dicke-type second-order quantum phase transition without the atom-atom interaction. Meanwhile, the atom-atom interaction makes the phase transition point shift to the lower atom-photon collective coupling strength.
We explore the quantum criticality of a two-site model combining quantum Rabi models with hopping interaction. Through a combination of analytical and numerical approaches, we find that the model allows the appearance of a superradiant quantum phase transition (QPT) even in the presence of strong A2{\mathbf{A}}^{2}A2 terms, preventing single-site superradiance. In the two-site model the effect of A2{\mathbf{A}}^{2}A2 terms can be surmounted by the photon delocalization from hopping, and a reversed superradiant QPT occurs as a consequence of the competition between A2{\mathbf{A}}^{2}A2 terms and the hopping interaction. We characterize the phase diagram and scaling functions and extract the critical exponents in the vicinity of the critical point, thus establishing the universal behavior of the second-order phase transition. Remarkably the effective hopping strength will be enhanced if more cavities are cascaded. We also prove that the multiqubit counterpart of the quantum Rabi dimer, i.e., the Dicke dimer, has the same properties in beating the A2{\mathbf{A}}^{2}A2 effect. Our work provides a path to the study of phase transitions in the presence of the A2{\mathbf{A}}^{2}A2 terms and offers the prospect of investigating quantum-criticality physics and quantum devices in many-body systems.