Electron spin ensemble strongly coupled to a three-dimensional microwave cavity

Abstract: We demonstrate the strong coupling between an electron spin ensemble and a three-dimensional cavity in a reflection geometry. We also find that an anticrossing in the cavity/spin spectrum can be observed under conditions that the collective coupling strength $g_c$ is smaller than the spin linewidth $\gamma_s$ or the cavity linewidth. We identify a ratio of $g_c$ to $\gamma_s$ ($g_c/\gamma_s >$ 0.64) as a condition to observe a splitting in the cavity frequency. Finally, we confirm that $g_c$ scales with $\sqrt{N}$, where $N$ is the number of polarized spins.