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 ErFeO₃, where the role of atoms (photons) is played by Er³⁺ spins (Fe³⁺ 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.

迪克模型描述了两能级原子集合与单模光子场的协同相互作用，并展示了作为光-物质耦合强度函数的量子相变。通过纳入短程原子-原子相互作用来扩展该模型使问题变得棘手，但预计会产生新的物理现象和相。在这里，我们使用 ErFeO ₃晶体模拟这样的扩展迪克模型，其中原子（光子）的作用由 Er ³⁺自旋（Fe ³⁺磁振子）发挥。通过太赫兹光​​谱和磁热效应测量作为温度和磁场的函数，我们证明了除了标准迪克模型预期的超辐射相和法向相之外，还存在一种新型原子有序相。此外，我们阐明了温度-磁场相图中相界的性质，识别了一级和二级相变。这些结果为使用充分表征的多体固态系统研究多原子量子光学模型奠定了基础。