Ultrastrong Coupling between Electron Paramagnetic Resonance and Cavity Photons

The Dicke model in quantum optics describes the cooperative interaction of an ensemble of two-level atoms with a single mode of light. Recently, ultrastrong coupling (USC) has been achieved in a wide range of light–matter hybrid systems. However, the matter side of the coupled system is usually viewable as a bosonic excitation, and thus temperature-independent boson–boson models can describe observed USC phenomena. In addition, the USC of magnetic resonances with cavities remains largely unexplored. Here, we study the USC of an ensemble of paramagnetic spins with Fabry–Pérot (FP) cavity photons in Gd₃Ga₅O₁₂ (GGG), a paramagnetic insulator, in the presence of an external magnetic field. We found that the cavity photon–EPR (electron paramagnetic resonance) coupling strength is dependent not only on the magnetic field but also on the temperature via Pauli’s principle, a fermionic character. We used terahertz time-domain spectroscopy in magnetic fields up to 30 T for probing polariton branches both in the bulk and thin-film limits. In the bulk case, where no particular FP mode is defined, we observed that the coupling of EPR with free-space THz photons reached the USC regime at high magnetic fields and low temperatures. In the thin-film limit, we found that the coupling between the second FP mode and EPR can reach the USC regime at room temperature.