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Journal of Physics B Atomic Molecular and Optical Physics

Study of phase transition, dynamical chaos and Loschmidt echo by using a parametrically driven cavity-magnon hybrid system

Z L Li, Hong-Yu Chen, Jiang Xue-huan, Sui Ji-Xiang, Huang Hai-bo, Xiu-Juan Dong, Kai Chen, Cheng Chen, Yuan Zhou

Published Jul 9, 2026• 0 citations
Publisher

Abstract

Abstract In this work, we investigate quantum phase transitions (QPTs), dynamical chaos and Loschmidt echo (LE) behaviors in a parametrically driven cavity-magnon hybrid system. The system consists of a yttrium iron garnet microsphere coupled to a microwave cavity with a squeezed cavity field generated via an optical parametric amplification process, and is described by an extended Tavis–Cummings model. Using the Holstein–Primakoff (HP) transformation and displacement transformation, we derive the ground-state energy function and obtain the phase diagram. The results show that the system undergoes a second-order QPT between the normal phase and the superradiant phase in the thermodynamic limit. Once the system enters the SP region, this design will induce a strong nonlinearity, thereby exhibiting significant chaotic dynamic behavior, verified by the Poincaré section method. Furthermore, we introduce the LE method to this hybrid system in order to characterize its QPT behaviors. With the assistance of the auxiliary atoms, the observable parameter LE exhibits consistency with the QPT laws, which can be used to effectively detect the critical behavior of this magnon-photon system. This work reveals the laws of phase transitions, dynamical chaos and LE behaviors in a parametrically driven cavity-magnon hybrid system, providing a theoretical basis for simulating and exploring quantum critical phenomena, nonlinear behaviors and quantum measurements in hybrid magnon systems.

DOI
10.1088/1361-6455/ae889b

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Abstract In this work, we investigate quantum phase transitions (QPTs), dynamical chaos and Loschmidt echo (LE) behaviors in a parametrically driven cavity-magnon hybrid system. The system consists of a yttrium iron garnet microsphere coupled to a microwave cavity with a squeezed cavity field generated via an optical parametric amplification process, and is described by an extended Tavis–Cummings model. Using the Holstein–Primakoff (HP) transformation and displacement transformation, we derive the ground-state energy function and obtain the phase diagram. The results show that the system undergoes a second-order QPT between the normal phase and the superradiant phase in the thermodynamic limit. Once the system enters the SP region, this design will induce a strong nonlinearity, thereby exhibiting significant chaotic dynamic behavior, verified by the Poincaré section method. Furthermore, we introduce the LE method to this hybrid system in order to characterize its QPT behaviors. With the assistance of the auxiliary atoms, the observable parameter LE exhibits consistency with the QPT laws, which can be used to effectively detect the critical behavior of this magnon-photon system. This work reveals the laws of phase transitions, dynamical chaos and LE behaviors in a parametrically driven cavity-magnon hybrid system, providing a theoretical basis for simulating and exploring quantum critical phenomena, nonlinear behaviors and quantum measurements in hybrid magnon systems.
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.
Preparing magnon nonclassical states is a central topic in the study of quantum magnonics. Here we propose to generate magnon squeezed states in a hybrid cavity-magnon-qubit system by engineering an effective Rabi-type magnon-qubit interaction. This is achieved by adiabatically eliminating the cavity mode and driving the qubit with two microwave fields, of which the driving frequencies and amplitudes are properly selected. By operating the system around the critical point associated with the ground-state superradiant phase transition in the normal phase, a magnon parametric amplification-like interaction is induced, leading to a dynamical magnon squeezing. We further analyze the effects of the dissipation, dephasing, and thermal noise on the magnon squeezing. Our results indicate that a moderate degree of squeezing can be produced using currently available parameters in the experiments.
Abstract It belongs to a hot topic to sense or detect the weak and even ultra-weak physical quantities by utilizing quantum platforms and methods. We here propose a hybrid magnon-photon system of the yttrium iron garnet (YIG) magnon mode coupled to a microwave cavity, which also includes another degree of freedom with respect to the thermal vibration of this YIG microsphere. In this quasi-tripartite coupling system, we generalize the condition for satisfying energy degeneracy and anti-crossing behaviors. Especially around the zero-energy area, we can get the joint quantum effects of anti-crossing behavior and degeneracy of systemic energy, and then reach a significantly enhanced sensitivity to this phase disturbance. Therefore our proposal can characterize this weak vibration through a phase disturbance and indicate a group of clearly resolvable output spectra. This investigation may be considered as an encouraging attempt on sensing weak quantity by engineering the systemic energy into the critical area for further enlarging its sensitivity to the weak disturbance.
In recent years, the cavity quantum photomechanics has been developed rapidly, and played a very important role in quantum information processing, quantum basic principle verification, and high-precision measurement. The kinds of quantum mechanical behaviors have also been explored and discovered in the study of cavity mechanics. By placing the Kerr medium in the system, quantum nonlinearity is introduced into the optomechanical system. Quantum phase transition is a relatively important part in the research of condensed matter physics. Since Dicke quantum phase transition was successfully observed experimentally, the problem of quantum phase transition in the optical cavity has attracted more attention. The spin-coherent-state variation method and the Holstein-Primakoff transformation are used to theoretically calculate the ground state energy functional, and the rich structure of the macroscopic multi-particle quantum state is given by adjusting the parameters. The quantum phase transition evolution equation describes the relationship between each phase and the time of generating a new phase when reaching the critical phase transition point. At the same time, the mode squeezing of multi-mode hybrid optomechanical system has also became one of the basic problems of quantum mechanical behavior in cavity quantum dynamics. In this article, we explore the quantum dynamics of optomechanical devices including single-cavity and dual-cavities. We find that the system will undergo a dynamic phase transition, which is similar to the Dicke-Hepp-Lieb superradiant type phase transition, and a new dynamic critical point appears in the coupling between the momentum quadratures of the two optical fields. By manipulating the coupling parameters, we can achieve selective energy exchange between any two modes and the critical coupling point corresponds to selective energy exchange. Mode squeezing, which is easy to measure by applying the quantum uncertainty relationship, is also revealed and consistent with selective energy exchange. The study of coordinate and momentum variances gives us the revelation that the compressed orthogonal variables are the most suitable for measurement because of the small quantum noise. In fact, phononic modes can store energy in a longer duration, while photonic modes can transfer energy in a long distance. This phenomenon makes the hybrid optomechanical cavities useful in the next-generation quantum communications and quantum information processing units.
Abstract Quantum phase transition (QPT) in the Dicke model has long attracted considerable interest due to its fundamental importance in quantum optics and many-body physics. Recent studies indicate that QPT-like behavior may also arise in the driven Tavis-Cummings (TC) model—a simplified variant of the Dicke model that neglects counter-rotating-wave coupling terms. Hybrid quantum systems, capitalizing on the advantages of different components, offer a promising platform to realize such many-body systems. Here, we experimentally observe a dissipative phase transition in the thermodynamic limit using a driven TC model, implemented by coupling an electron spin ensemble to a superconducting microwave resonator. This QPT behavior is detected via the measurements of Rabi splitting, which exhibits a unique dependence on the collective spin excitations of the system. Our findings provide a route to experimentally investigate critical phenomena in realistic many-body systems under decoherence, and promise potential applications in quantum simulation and other emerging quantum technologies.
We propose a scheme to engineer the superradiant phase transition (SPT) in cavity magnonics by periodically modulating the frequency of the magnon mode. The studied system is composed of a yttrium iron garnet (YIG) sphere positioned inside a microwave cavity, where magnons in the YIG sphere are strongly coupled to microwave photons. Under the Floquet drive, the effective frequencies of both the cavity and magnon modes can be readily controlled via the frequency and strength of Floquet field. This tunability allows the cavity magnonic system to support a rich steady-state phase diagram, featuring parity-symmetric, parity-symmetry-broken, bistable, and unstable phases. With the increase of Floquet-field strength, the system exhibit a discontinuous phase transition from the parity-symmetric phase to the parity-symmetry-broken phase at a critical threshold, accompanied by an abrupt jump of the magnon occupation from zero to a finite value. Upon further increase of Floquet-field strength, the magnon occupation declines continuously from a nonzero value back to zero, corresponding to a second-order phase transition that restores the parity-symmetric phase. Additionally, fluctuations in magnon number during the SPT process are examined. Our work establishes an alternative route to engineer the cavity-magnon SPT without relying on microwave parametric drive.