Observation of Dicke cooperativity in magnetic interactions

The interaction of N two-level atoms with a single-mode light field is an extensively studied many-body problem in quantum optics, first analyzed by Dicke in the context of superradiance. A characteristic of such systems is the cooperative enhancement of the coupling strength by a factor of N. In this study, we extended this cooperatively enhanced coupling to a solid-state system, demonstrating that it also occurs in a magnetic solid in the form of matter-matter interaction. Specifically, the exchange interaction of N paramagnetic erbium(III) (Er 3+ ) spins with an iron(III) (Fe 3+ ) magnon field in erbium orthoferrite (ErFeO 3 ) exhibits a vacuum Rabi splitting whose magnitude is proportional to N. Our results provide a route for understanding, controlling, and predicting novel phases of condensed matter using concepts and tools available in quantum optics.