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arXiv:2412.08305 · Physical Review A

Superradiant phase transitions in the quantum Rabi model: Overcoming the no-go theorem through anisotropy

Ye Tian, Yanzhi Wang, Xiang-You Chen, Qing‐Hu Chen, Haiqing Lin

Published Apr 25, 2025• 11 citations
arXivHTMLPDF

Abstract

Although the superradiant phase transition (SRPT) is prohibited in the paradigmatic quantum Rabi model due to the no-go theorem caused by the ${\mathbf{A}}^{2}$ term, we demonstrate two distinct types of SRPTs emerging from the normal phase in the anisotropic quantum Rabi model. A discontinuous phase transition between the two types of superradiant phases also emerges in the presence of a strong ${\mathbf{A}}^{2}$ term. Additionally, a rich phase diagram featuring a triple point, which connects first- and second-order phase transitions, is derived analytically and confirmed through numerical diagonalization at large effective system sizes. Finally, distinct critical behavior at the triple point is revealed and contrasted with that of a single continuous SRPT. This work may open a new avenue for observing SRPTs in their intrinsic form without altering the ${\mathbf{A}}^{2}$ term, while also offering a practical platform for exploring rich quantum phenomena.

DOI
10.1103/physreva.111.043716

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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
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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.
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.
In this manuscript, we analyze the mechanism of the superradiant phase transition in the anisotropic Rabi model under the classical oscillator limit using the pattern picture. By expanding the anisotropic Rabi model Hamiltonian in operator space, we obtained three patterns, and we find that the phase transition arises from the competition between patterns. The difficulty in achieving the classical oscillator limit motivates our investigation into the quantum phase transition within a parametrically-driven Jaynes-Cummings model. This parametrically-driven Jaynes-Cummings model can reproduce the dynamics of an ultrastrong-coupling anisotropic Rabi model in a squeezed-light frame. According to the eigenenergies and eigenstates of the normal and superradiant phases of this equivalent anisotropic Rabi model, we find that the excitation energy of the normal phase and the superradiant phase vanishes at the critical point. The photon number becomes infinite beyond the critical point. These results indicate that the system undergoes a superradiant phase transition at the critical point.