Marquez Peraca, NicolasLi, XinweiMoya, Jaime M.Hayashida, KenjiKim, DasomMa, XiaoxuanNeubauer, Kelly J.Fallas Padilla, DiegoHuang, Chien-LungDai, PengchengNevidomskyy, Andriy H.Pu, HanMorosan, EmiliaCao, ShixunBamba, MotoakiKono, Junichiro2024-09-102024-09-102024Marquez Peraca, N., Li, X., Moya, J. M., Hayashida, K., Kim, D., Ma, X., Neubauer, K. J., Fallas Padilla, D., Huang, C.-L., Dai, P., Nevidomskyy, A. H., Pu, H., Morosan, E., Cao, S., Bamba, M., & Kono, J. (2024). Quantum simulation of an extended Dicke model with a magnetic solid. Communications Materials, 5(1), 1–9. https://doi.org/10.1038/s43246-024-00479-3https://hdl.handle.net/1911/117869The 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.engExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license.  Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Journal articles43246-024-00479-3https://doi.org/10.1038/s43246-024-00479-3