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arXiv:2610.35445

Multistability and Critical Frustrated Superradiance in Open Anisotropic Quantum Rabi Trimer

Ya-Ping Ni, Yi-Ge Wu, Jie-Qiao Liao, Jin-Feng Huang

quant-phSubmitted Oct 26, 2026• Announced Oct 27, 2026• 0 citations• Revised Oct 27, 2026 (v2)
v1 · Oct 26, 2026v2 · Oct 27, 2026
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Abstract

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.

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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.
We investigate the nonequilibrium steady state of the anisotropic open quantum Rabi model, which exhibits first-order and second-order dissipative phase transitions upon varying the degree of anisotropy between the coupling strengths of rotating and counter-rotating terms. Using both semiclassical and quantum approaches, we find a rich phase diagram resulting from the interplay between the anisotropy and the dissipation. First, there exists a bistable phase where both the normal and superradiant phases are stable. Second, there are multicritical points where the phase boundaries for the first- and second-order phase transitions meet. We show that a new set of critical exponents governs the scaling of the multicritical points. Finally, we discuss the feasibility of observing the multicritical transitions and bistability using a pair of trapped ions where the anisotropy can be tuned by controlling the intensity of the Raman transitions. Our study enlarges the scope of critical phenomena that may occur in finite-component quantum systems, which could be useful for applications in critical quantum sensing. Published by the American Physical Society 2024
We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N>1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N=1 up to the thermodynamic limit.
Emergence of Rich Dissipative Phases in the Anisotropic Quantum Rabi Model Driven by the A2A^2A2 Term
The open anisotropic quantum Rabi model (QRM) is studied in this work, with an explicit A2A^2A2 term incorporated. It is shown that, in the presence of cavity loss, anisotropy allows the steady-state superradiant transition to occur even when the A2A^2A2 term prohibits the transition in the isotropic case. The A2A^2A2 term reshapes and enriches the known steady-state phase diagram of the open anisotropic QRM, leading to an asymmetric structure composed of normal, superradiant, and bistable phases. In particular, the nonequilibrium tricritical points are generally separated from the merger point of the two critical branches that bound the superradiant region. Isolated bistable regions also emerge, and the number and positions of tricritical points are reduced. Notably, the anomalous photon-number fluctuation scaling is associated with the merger of the two critical branches, rather than with the tricritical points. These results clarify the role of the A2A^2A2 term contribution in the steady-state structure of the open anisotropic QRM and provide a refined extension of the previously known dissipative phase diagram, offering a useful theoretical reference for future studies of related open light--matter systems.
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.
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.
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.