Collective strong coupling with homogeneous Rabi frequencies using a 3D lumped element microwave resonator

We design and implement 3D-lumped element microwave cavities that spatially focus magnetic fields to a small mode volume. They allow coherent and uniform coupling to electron spins hosted by nitrogen vacancy centers in diamond. We achieve large homogeneous single spin coupling rates, with an enhancement of more than one order of magnitude compared to standard 3D cavities with a fundamental resonance at 3 GHz. Finite element simulations confirm that the magnetic field distribution is homogeneous throughout the entire sample volume, with a root mean square deviation of 1.54%. With a sample containing 1017 nitrogen vacancy electron spins, we achieve a collective coupling strength of Ω = 12 MHz, a cooperativity factor C = 27, and clearly enter the strong coupling regime. This allows to interface a macroscopic spin ensemble with microwave circuits, and the homogeneous Rabi frequency paves the way to manipulate the full ensemble population in a coherent way.