Coherent Rabi dynamics of a superradiant spin ensemble in a microwave cavity

We achieve the strong-coupling regime between an ensemble of phosphorus donor spins in a highly enriched ²⁸Si crystal and a 3D dielectric resonator. Spins are polarized beyond Boltzmann equilibrium using spin-selective optical excitation of the no-phonon bound exciton transition resulting in N = 3.6 × 10¹³ unpaired spins in the ensemble. We observe a normal mode splitting of the spin-ensemble-cavity polariton resonances of 2g √ N = 580 kHz (where each spin is coupled with strength g) in a cavity with a quality factor of 75 000 (γ ≪ κ ≈ 60 kHz, where γ and κ are the spin dephasing and cavity loss rates, respectively). The spin ensemble has a long dephasing time (T^* ₂ = 9 μs) providing a wide window for viewing the dynamics of the coupled spin-ensemble-cavity system. The free-induction decay shows up to a dozen collapses and revivals revealing a coherent exchange of excitations between the superradiant state of the spin ensemble and the cavity at the rate g √ N. The ensemble is found to evolve as a single large pseudospin according to the Tavis-Cummings model due to minimal inhomogeneous broadening and uniform spin-cavity coupling. We demonstrate independent control of the total spin and the initial Z projection of the psuedospin using optical excitation and microwave manipulation, respectively. We vary the microwave excitation power to rotate the pseudospin on the Bloch sphere and observe a long delay in the onset of the superradiant emission as the pseudospin approaches full inversion. This delay is accompanied by an abrupt p-phase shift in the peusdospin microwave emission. The scaling of this delay with the initial angle and the sudden phase shift are explained by the Tavis-Cummings model.