Echo Trains in pulsed electron spin resonance*

Strong coupling between a spin ensemble and a microwave resonator is essential for a coherent exchange of excitation. While most experiments today focus on continuous wave experiments, we investigate the dynamics of the coupled spin-resonator system in the strong coupling regime. In particular, we use Hahn echos and observe multiple unexpected echo signatures after the first conventional echo. Experimentally, we study an ensemble of phosphorus donor spins in isotopically purified ²⁸Si with ms coherence times. With a static magnetic field, we tune their transition frequency into resonance with a superconducting lumped element microwave resonator. We present experimental data within and outside the strong coupling regime and discuss a model predicting and corroborating the amplitude evolution of the echos based on the echo separation time, the dephasing rate of the spin ensemble, and the linewidth of the microwave resonator.