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Physica Scripta

Reflect magnetic control of NV center’s ground-state energy structure through quantum phase transitions in a three-level system

Hao Jiang, Zeyun Shi, Yao Ou, Fazal Badshah, Zhou Xiao, Dong‐Yan Lü, Dong‐Yan Lü, Kai Chen, Cheng Chen, Yuan Zhou

Published Mar 6, 2026• 5 citations
Publisher

Abstract

Abstract We theoretically investigate the quantum phase transitions of a hybrid quantum system consisting of an ensemble of nitrogen-vacancy (NV) centers coupled to two microwave cavity resonators. By leveraging the Zeeman effect with a static magnetic field, we achieve a tunable switch between different three-level Dicke model configurations. We map out the global ground-state phase diagram and identify three distinct operating regimes: (i) a V type regime characterized by the competition between two superradiant phases, (ii) an effective two-level regime emerging near the level-crossing point due to channel decoupling and (iii) a cascade Ξ type regime induced by level inversion. Particularly in the cascade regime, we analyze a mechanism of ‘sequential phase transition’, where the onset of the second superradiant phase is strictly contingent upon the condensation of the first channel. This mechanism leads to a nested structure in the phase diagram, which is fundamentally distinct from the phase competition observed in V type systems. Furthermore, by calculating the excitation spectra, we observe the emergence of soft modes at continuous critical points, establishing the second-order quantum nature of the relevant transitions. Our proposal provides a feasible solid-state platform for simulating multicritical phenomena and realizing controllable light–matter interactions.

DOI
10.1088/1402-4896/ae4e6a

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Abstract We theoretically investigate the quantum phase transitions of a hybrid quantum system consisting of an ensemble of nitrogen-vacancy (NV) centers coupled to two microwave cavity resonators. By leveraging the Zeeman effect with a static magnetic field, we achieve a tunable switch between different three-level Dicke model configurations. We map out the global ground-state phase diagram and identify three distinct operating regimes: (i) a V type regime characterized by the competition between two superradiant phases, (ii) an effective two-level regime emerging near the level-crossing point due to channel decoupling and (iii) a cascade Ξ type regime induced by level inversion. Particularly in the cascade regime, we analyze a mechanism of ‘sequential phase transition’, where the onset of the second superradiant phase is strictly contingent upon the condensation of the first channel. This mechanism leads to a nested structure in the phase diagram, which is fundamentally distinct from the phase competition observed in V type systems. Furthermore, by calculating the excitation spectra, we observe the emergence of soft modes at continuous critical points, establishing the second-order quantum nature of the relevant transitions. Our proposal provides a feasible solid-state platform for simulating multicritical phenomena and realizing controllable light–matter interactions.
Abstract A theoretical scheme is proposed to simulate the quantum phase transitions (QPTs) of the three-level Dicke model. In this designed hybrid system, an ensemble of solid-state spins can simultaneously couple to a superconducting microwave (MW) resonator and a surface-acoustic-wave (SAW) cavity, and then ensure the simulation of the Λ type Dicke model with the acoustic-MW dual-channel transitions. Using a generalized Holstein-Primakoff (HP) mapping in the thermodynamic limit, we derive an effective Hamiltonian that preserves a Z 2 × Z 2 parity symmetry and therefore potentially supports a rich phase diagram. We obtain analytic expressions for the critical couplings of the three phases: the normal, superradiant I and superradiant II phases. We obtain analytic expressions for the critical couplings of three phases: the normal, superradiant I, and superradiant II phases. Among these, we can deterministically identify both first-order (discontinuous) and second-order (continuous) quantum phase transitions with distinct boundary characteristics. Additionally, rigorous diagonalization of the quadratic fluctuation Hamiltonian yields four excitation energies, whose behaviors further clarify the order and continuity of each phase transition. This attempt opens an interesting avenue for simulating multilevel QPTs by jointly using different coupling transducers, including acoustics, mechanics, magnons, and electromagnetics.
Generalized Dicke models can be implemented in hybrid quantum systems built from ensembles of nitrogen-vacancy (NV) centers in diamond coupled to superconducting microwave cavities. By engineering cavity assisted Raman transitions between two spin states of the NV defect, a fully tunable model for collective light-matter interactions in the ultrastrong coupling limit can be obtained. Our analysis of the resulting nonequilibrium phases for a single cavity and for coupled cavity arrays shows that different superradiant phase transitions can be observed using existing experimental technologies, even in the presence of large inhomogeneous broadening of the spin ensemble. The phase diagram of the Dicke lattice model displays distinct features induced by dissipation, which can serve as a genuine experimental signature for phase transitions in driven open quantum systems.
We propose an efficient scheme for simulating the Lipkin-Meshkov-Glick (LMG) model with nitrogen-vacancy (NV) center ensembles in diamond magnetically coupled to superconducting coplanar waveguide cavities. With the assistance of external microwave driving fields, we show that the interaction of the NV spins can be easily controlled, and several types of the LMG model can be realized by tuning the different parameters. Under the thermal dynamical limit, the distinct nonequilibrium second-order quantum phase transition of the spin ensemble can be achieved at the critical point. Furthermore, we show that the spin squeezed state can be generated by tailoring the LMG Hamiltonian to possess the two-axis countertwisting form in this hybrid quantum system.
Abstract Quantum phase transitions with multicritical points are fascinating phenomena occurring in interacting quantum many-body systems. However, multicritical points predicted by theory have been rarely verified experimentally; finding multicritical points with specific behaviors and realizing their control remains a challenging topic. Here, we propose a system that a quantized light field interacts with a two-level atomic ensemble coupled by microwave fields in optical cavities, which is described by a generalized Dicke model. Multicritical points for the superradiant quantum phase transition are shown to occur. We determine the number and position of these critical points and demonstrate that they can be effectively manipulated through the tuning of system parameters. Particularly, we find that the quantum critical points can evolve into a Lifshitz point (LP) if the Rabi frequency of the light field is modulated periodically in time. Remarkably, the texture of atomic pseudo-spins can be used to characterize the quantum critical behaviors of the system. The magnetic orders of the three phases around the LP, represented by the atomic pseudo-spins, are similar to those of an axial next-nearest-neighboring Ising model. The results reported here are beneficial for unveiling intriguing physics of quantum phase transitions and pave the way towards to find novel quantum multicritical phenomena based on the generalized Dicke model.
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.
Abstract The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating short-range atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO 3 , where the role of atoms (photons) is played by Er 3+ spins (Fe 3+ magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magnetic-field phase diagram, identifying both first-order and second-order phase transitions. These results lay the foundation for studying multiatomic quantum optics models using well-characterized many-body solid-state systems.