Gain-compensated cavities for the dynamic control of light-matter interactions

We propose an efficient approach for actively controlling the Rabi oscillations in emitter-cavity hybrids based on the presence of an element with optical gain. Inspired by recent developments in parity-time ($\mathcal{PT}$)-symmetry photonics, we show that nano- or micro-cavities where intrinsic losses are partially or fully compensated by an externally controllable amount of gain offer unique capabilities for manipulating the dynamics of emitters. In particular, one can drastically modify the dynamics of the system, increase the overall occupation numbers, enhance the longevity of the Rabi oscillations, and even decelerate them to the point where their experimental observation becomes less challenging. Furthermore, we show that there is a specific gain value that leads to an exceptional point, where both emitter and cavity occupation oscillate practically in phase, with occupation numbers that can significantly exceed unity. By revisiting a recently-introduced Rabi-visibility measure, we provide robust guidelines for quantifying the coupling strength and achieving strong-coupling with adaptable Rabi frequency via loss compensation.