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arXiv:2509.00695 · Chinese Physics B

Parametrically driven superradiance of an interacting Tavis–Cummings model

Wen-Jie Geng, Yi‐Wen Han, Wei Yi

Published Nov 6, 2025• 1 citation
arXivHTMLPDF

Abstract

Abstract We consider the superradiant transition of a generalized Tavis–Cummings model, where a number of two-level qubits are coupled to a dissipative cavity. The cavity is coherently driven through a parametric medium, and all-to-all interactions between the qubits are introduced. While the nonlinear gain from the parametric drive breaks the U (1) symmetry of the standard Tavis–Cummings model, thus giving rise to superradiance with squeezed cavity fields, we show that the interactions impact the collective excitations and significantly modify the superradiant transition. Insights into the superradiant phase transitions, as well as the interaction effects, are obtained through effective models involving only a handful of low-lying collective states, under which the steady-state phase diagram of the hybrid system is faithfully reproduced. Our study is relevant to Rydberg-atom arrays coupled to a parametrically driven cavity, where the long-range interactions derive from the dipole–dipole interatomic interactions.

DOI
10.1088/1674-1056/ae1c33

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Abstract We consider the superradiant transition of a generalized Tavis–Cummings model, where a number of two-level qubits are coupled to a dissipative cavity. The cavity is coherently driven through a parametric medium, and all-to-all interactions between the qubits are introduced. While the nonlinear gain from the parametric drive breaks the U (1) symmetry of the standard Tavis–Cummings model, thus giving rise to superradiance with squeezed cavity fields, we show that the interactions impact the collective excitations and significantly modify the superradiant transition. Insights into the superradiant phase transitions, as well as the interaction effects, are obtained through effective models involving only a handful of low-lying collective states, under which the steady-state phase diagram of the hybrid system is faithfully reproduced. Our study is relevant to Rydberg-atom arrays coupled to a parametrically driven cavity, where the long-range interactions derive from the dipole–dipole interatomic interactions.
Abstract We investigate the steady-state quantum phases and associated collective phenomena of an open Tavis–Cummings (TC) model driven by a two-photon source. The standard (non-dissipative) TC model describes the quantum phases of an ensemble of N q two-level quantum emitters interacting with a single-mode electromagnetic field. The interplay among coherent driving, dissipation, and dipole interactions of the open TC model results in emergent collective phenomena, leading to a dissipative or non-equilibrium phase transition from the normal to the superradiant phase. We solve the Liouvillian equation analytically using the semi-classical mean-field approximation. We carry out stability analysis of the steady-state phases and determine the phase boundary. The use of Holstein–Primakoff transformation in the thermodynamic limit N q → ∞ reduces the system to an effective coupled-oscillator model, the solution of which yields collective modes.
We study the quantum metric in a driven Tavis-Cummings model, comprised of multiple qubits interacting with a quantized photonic field. The parametrical driving of the photonic field breaks the system’s U(1) symmetry down to a Z 2 symmetry, whose spontaneous breaking initiates a superradiant phase transition. We analytically solved the eigenenergies and eigenstates, and numerically simulated the system behaviors near the critical point. The critical behaviors near the superradiant phase transition are characterized by the quantum metric, defined in terms of the response of the quantum state to variation of the control parameter. In addition, a quantum metrological protocol based on the critical behaviors of the quantum metric near the superradiant phase transition is proposed, which enables greatly the achievable measurement precision.
We study the superradiant phase transition of an array of Rydberg atoms in a dissipative microwave cavity. Under the interplay of the cavity field and the long-range Rydberg interaction, the steady state of the system exhibits an interaction-enhanced superradiance, with vanishing critical atom-cavity coupling rates at a discrete set of interaction strengths. We find that, while the phenomenon can be analytically understood in the case of a constant all-to-all interaction, the enhanced superradiance persists under typical experimental parameters with spatially dependent interactions, but at modified critical interaction strengths. The diverging susceptibility at these critical points is captured by emergent quantum Rabi models, each of which comprises a pair of collective atomic states with different numbers of atomic excitations. These collective states become degenerate at the critical interaction strengths, resulting in a superradiant phase for an arbitrarily small atom-cavity coupling.
Dissipation can fundamentally reconstruct the multicritical structure of driven-dissipative light–matter systems. In the interpolating Dicke–Tavis–Cummings model, cavity loss eliminates the U(1)-symmetric superradiant phase on the Tavis–Cummings line λx=λy and splits the original multicritical point into a pair of dissipation-induced tricritical points. Here, we show that intracavity optical squeezing provides a coherent means of continuously reshaping this loss-generated multicritical structure. The single-mode parametric interaction acts asymmetrically on the two cavity quadratures, thereby deforming the phase boundaries and continuously tuning the dissipation-induced tricritical points. We analytically determine the phase boundaries and the evolution of the tricritical structure with the parametric gain and cavity dissipation, and show that the two tricritical points coalesce in the weak-loss limit. Photon-number fluctuations provide clear quantum signatures of the squeezing-controlled multicritical structure.
Entanglement and quantum correlations between atoms are not usually considered key ingredients of the superradiant phase transition. Here we consider the Tavis-Cummings model, a solvable system of two-levels atoms, coupled with a single-mode quantized electromagnetic field. This system undergoes a superradiant phase transition, even in a finite-size framework, accompanied by a spontaneous symmetry breaking, and an infinite sequence of energy level crossings. We find approximated expressions for the ground state, its energy, and the position of the level crossings, valid in the limit of a very large number of photons with respect to that of the atoms. In that same limit, we find that the number of photons scales quadratically with the coupling strength, and linearly with the system size, providing a new insight into the superradiance phenomenon. Resorting to novel multipartite measures, we then demonstrate that this quantum phase transition is accompanied by a crossover in the quantum correlations and entanglement between the atoms (qubits). The latters therefore represent suited order parameters for this transition. Finally, we show that these properties of the quantum phase transition persist in the thermodynamic limit.
We theoretically investigate the quantum phase transition in the collective systems of qubits in a high quality cavity, where the cavity field is squeezed via the optical parametric amplification process. We show that the squeezed light induced symmetry breaking can result in quantum phase transition without the ultrastrong coupling requirement. Using the standard mean field theory, we derive the condition of the quantum phase transition. Surprisingly, we show that there exists a tricritical point where the first- and second-order phase transitions meet. With specific atom-cavity coupling strengths, both the first- and second-order phase transition can be controlled by the nonlinear gain coefficient, which is sensitive to the pump field. These features also lead to an optical switching from the normal phase to the superradiant phase by just increasing the pump field intensity. The signature of these phase transitions can be observed by detecting the phase space Wigner function distribution with different profiles controlled by the squeezed light intensity. Such superradiant phase transition can be implemented in various quantum systems, including atoms, quantum dots, and ions in optical cavities as well as the circuit quantum electrodynamics system.