Coherent Rabi Dynamics of a Superradiant Spin Ensemble in a Microwave Cavity

Abstract

We achieve the strong-coupling regime between an ensemble of phosphorus donor spins in a highly enriched ^{28}Si 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=3.6×10^{13} unpaired spins in the ensemble. We observe a normal mode splitting of the spin-ensemble–cavity polariton resonances of 2gsqrt[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 gsqrt[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 π-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.