Anomalous Purcell decay of strongly driven and disordered emitters coupled to a cavity (Part 2): Theory

Arrays of quantum emitters interacting with cavities offer insights into the interplay of many-body quantum dynamics and collective emission. Motivated by recent experimental progress, we study a disordered ensemble of spins realized with Er3+ ions coupled to a laser-driven nanophotonic cavity. The light emission from the cavity following an initial excitation pulse exhibits a non-trivial reduction at cavity resonance, leading to a double-peak structure reminiscent of vacuum Rabi splitting, but persistent at long times and dependent on initial excitation power. These observations suggest a non-trivial modification of conventional Purcell decay physics in this strongly driven, strongly disordered system. We theoretically characterize the dynamics of the light field and collective spin observables with a variety of techniques, including semi-classical approaches and Holstein-Primakoff mappings. The role of collective effects and spin-spin interactions mediated by the cavity is identified and characterized. Comparisons of the theory to the experimental data are made