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 were polarized beyond Boltzmann equilibrium using spin selective optical excitation of the no-phonon bound exciton transition resulting in $N$ = $3.6\cdot 10^{13}$ unpaired spins in the ensemble. We observed a normal mode splitting of the spin ensemble-cavity polariton resonances of 2$g\sqrt{N}$ = 580 kHz (where each spin is coupled with strength $g$) in a cavity with a quality factor of 75,000 (${\hat{I}}^3\ll \hat{I}º\approx$ 60 kHz where ${\hat{I}}^3$ and $\hat{I}º$ are the spin dephasing and cavity loss rates, respectively). The spin ensemble has a long dephasing time (T${}_2^{\ast }$ = 9 $\hat{I}¼$s) 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 $g\sqrt{N}$. 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 $\ddot{I}€$ 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.

9 pages, 7 figures