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arXiv:2604.21820 · Physical Review A

Robust continuous symmetry breaking and multiversality in the chiral Dicke model

Nikolay Yegovtsev, Sayan Choudhury, W. Vincent Liu

quant-phcond-mat.quant-gasSubmitted Apr 23, 2026• Announced Apr 24, 2026• 0 citations
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Abstract

The Dicke model (DM) serves as a paradigm for understanding collective light-matter interactions. We introduce the chiral Dicke model, a generalization where an atomic ensemble couples to a two-mode cavity via chiral interactions. Unlike the standard DM, the chiral DM is endowed with an inherent continuous $U(1)$ symmetry associated with angular momentum conservation. The ground-state phase diagram and the associated quantum phase transitions are charted out, revealing a $U(1)$-broken superradiant phase that spans a broad parameter space. We demonstrate that the spectrum of quantum fluctuations is highly tunable in both the symmetric and broken phases. Strikingly, our calculations reveal that the system exhibits `multiversality', where distinct universality classes govern the transition between the same two phases. In particular, along a special line in parameter space, the dynamical critical exponent for the normal-superradiant phase transition changes from $zν=1$ to $zν=1/2$. Our work establishes the chiral Dicke model as a powerful platform to realize novel quantum phases and multiversal critical phenomena in light-matter coupled systems.

Comments
4 main pages + 3 suppl., 4 main figures + 1 suppl; comments are welcome

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The Dicke model (DM) serves as a paradigm for understanding collective light-matter interactions. We introduce the chiral Dicke model, a generalization where an atomic ensemble couples to a two-mode cavity via chiral interactions. Unlike the standard DM, the chiral DM is endowed with an inherent continuous U(1)U(1)U(1) symmetry associated with angular momentum conservation. The ground-state phase diagram and the associated quantum phase transitions are charted out, revealing a U(1)U(1)U(1)-broken superradiant phase that spans a broad parameter space. We demonstrate that the spectrum of quantum fluctuations is highly tunable in both the symmetric and broken phases. Strikingly, our calculations reveal that the system exhibits `multiversality', where distinct universality classes govern the transition between the same two phases. In particular, along a special line in parameter space, the dynamical critical exponent for the normal-superradiant phase transition changes from zν=1zν=1zν=1 to zν=1/2zν=1/2zν=1/2. Our work establishes the chiral Dicke model as a powerful platform to realize novel quantum phases and multiversal critical phenomena in light-matter coupled systems.
In an open, U(1)U(1)U(1)-symmetric Dicke model with chiral atom-cavity couplings, we show that dissipation drives two limit-cycle phases of opposite chirality in the thermodynamic limit, obtaining exact analytical solutions. These phases are separated by a U(1)U(1)U(1)-broken superradiant state, lending the phase diagram a topological character, and persist under U(1)U(1)U(1)-preserving perturbations, making them candidates for chiral continuous time crystals. In addition to stable normal and inverted steady states, the model also exhibits multistability, where the long-time dynamics is set by the initial state. Our results establish dissipation as a resource for inducing chiral dynamical order in light-matter coupled systems.
The Dicke model is a fundamental model of quantum optics, which describes the interaction between light and matter. In the Dicke model, the light component is described as a single quantum mode, while the matter is described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model shows a mean-field phase transition to a superradiant phase. This transition belongs to the Ising universality class and was realized experimentally in cavity quantum electrodynamics experiments. Although the superradiant transition bears some analogy with the lasing instability, these two transitions belong to different universality classes.
Interactions among emitters provide a powerful means of controlling collective light--matter phenomena, yet their role in superradiant criticality has not been thoroughly investigated. Here we construct a minimal model that can yield analytical insights --- a Dicke model with two interacting atoms coupled to a single mode cavity --- to study such interaction effects. We show that interaction changes the phase boundary, and may even completely suppress the atom-photon coupling threshold for superradiance and change the universality class of the phase transition. We further study the dissipative phase transition and quantum dynamics in the presence of dissipation channels such as photon loss and spin relaxation. Our results demonstrate important roles played by the atom-atom interaction and how it can be engineered to control atom-photon coupling.
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 study a generalization of a recently introduced Dicke trimer model [Phys. Rev. Lett. 128, 163601 (2022); Phys. Rev. Res. 5, L042016 (2023)], which allows for cavity losses and unbalanced light-matter interactions (in which rotating and counter-rotating terms can be tuned independently). In the original description of a Dicke trimer, three Dicke models are coupled in a ring topology via a complex photon hopping whose complex phase describes a synthetic magnetic field threading the loop. This original model features several intriguing equilibrium phases and critical phenomena such as frustrated superradiance, two-critical scalings in the frustrated superradiant phase, and finite critical fluctuations in the anomalous normal phase. Here, we find that in the extreme unbalanced limit, where only rotating terms are present, the U(1) symmetry of the Tavis-Cummings model is restored, qualitatively altering the critical phenomena in the superradiant phase due to the presence of a zero-energy mode. To analyze this general regime, we develop a semiclassical theory based on a requantization technique. This theory also provides further physical insight on recently reported anomalous finite critical fluctuations in the time-reversal broken regime. Moving to the open-Dicke case, by introducing local dissipation to the cavities, we observe the emergence of a rich range of nonequilibrium phases characterized by trivial and nontrivial dynamical signatures. In the former case, we identify, when time-reversal symmetry is present, a new stationary phase that features superradiant states in two of the three cavities and a normal state in the other cavity. In the latter case, we observe the emergence of dynamical phases in which the system exhibits superradiant oscillations, characterized by periodic or chaotic phase space patterns. The landscape of transitions associated with these dynamical phases features a wide range of qualitatively different behaviors such as Hopf bifurcations (followed by period-doubling cascades or quasiperiodic oscillations), anomalous Hopf bifurcations (with burst-oscillation-like post-bifurcation dynamics), collisions between basins of attraction (associated with different symmetry-broken equilibria), and exterior crises (featuring transient chaotic dynamics). We highlight how the two-critical-scalings feature of the closed model is robust under dissipation (with doubled critical exponents) while the phenomenon of anomalous finite critical fluctuations becomes a mean-field scaling (as a consequence of Hopf bifurcations of the equilibria featuring the normal state) in the open model.
The Dicke model can exhibit quantum phase transition between the normal and the superradiant phases when the strength of the light-matter coupling exceeds the ultrastrong-coupling regime. However, it is challenging to observe this phase transition in practical systems due to limited coupling strength or finite two-photon A2{A}^{2}A2 terms. Here we show that by applying a periodic modulation to the frequency of the two-level systems in a standard Dicke model in the strong-coupling regime, an anisotropic Dicke model with tunable rotating and counter-rotating terms in the ultrastrong-coupling regime can be achieved. We calculate the ground state and the excitation spectrum of this model in terms of the modulation parameters. Our result shows that the superradiant phases can be observed in cavity- or circuit-quantum electrodynamics systems with strong coupling.