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The Dicke model describes the cooperative interaction of an ensemble oftwo-level atoms with a single-mode photonic field and exhibits a quantum phasetransition as a function of light--matter coupling strength. Extending thismodel by incorporating short-range atom--atom interactions makes the problemintractable but is expected to produce new phases. Here, we simulate such anextended Dicke model using a crystal of ErFeO$_3$, where the role of atoms(photons) is played by Er$^{3+}$ spins (Fe$^{3+}$ magnons). Throughmagnetocaloric effect and terahertz magnetospectroscopy measurements, wedemonstrated the existence of a novel atomically ordered phase in addition tothe superradiant and normal phases that are expected from the standard Dickemodel. Further, we elucidated the nature of the phase boundaries in thetemperature--magnetic-field phase diagram, identifying both first-order andsecond-order phase transitions. These results lay the foundation for studyingmultiatomic quantum optics models using well-characterized many-body condensedmatter systems.

Quantum Simulation of an Extended Dicke Model with a Magnetic Solid