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

TL;DR

This paper demonstrates strong coupling between an electron spin ensemble and a 3D microwave cavity, revealing conditions for observing spectral splitting and confirming the collective coupling scales with the square root of the number of spins.

Contribution

It provides experimental evidence of strong coupling in a 3D cavity with electron spins and identifies the ratio of coupling strength to linewidth as a key condition for spectral splitting.

Findings

Spectral anticrossing observed even when coupling is weaker than linewidths.

The ratio g_c/γ_s > 0.64 is necessary for cavity frequency splitting.

g_c scales with the square root of the number of polarized spins.

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.