Probing strong coupling between a microwave cavity and a spin ensemble with Raman heterodyne spectroscopy

Raman heterodyne spectroscopy is a powerful tool for characterizing the energy and dynamics of spins. The technique uses an optical pump to transfer coherence from a spin transition to an optical transition where the coherent emission is more easily detected. Here Raman heterodyne spectroscopy is used to probe an isotopically purified ensemble of erbium dopants in a yttrium orthosilicate (Y₂SiO₅) crystal coupled to a microwave cavity. Because the erbium electron spin transition is strongly coupled to the microwave cavity, we observed Raman heterodyne signals at the resonant frequencies of the hybrid spin-cavity modes (polaritons) rather than the bare erbium spin-transition frequency. Using the coupled system, we made saturation recovery measurements of the ground-state spin relaxation time T₁ = 10±3 s and also observed Raman heterodyne signals using an excited state spin transition. We discuss the implications of these results for efforts toward converting microwave quantum states to optical quantum states.