Pushing Purcell enhancement beyond its limits

Purcell-enhanced photon emission into a cavity is at the heart of many schemes for interfacing quantum states of light and matter. We show that the intra-cavity coupling of orthogonal polarisation modes in a birefringent cavity allows for the emitter and photon to be decoupled prior to emission from the cavity mode, enabling photon extraction efficiencies that exceed the, previously considered fundamental, limits of Purcell enhancement. Tailored cavity birefringence is seen to mitigate the tradeoff between stronger emitter-cavity coupling and efficient photon extraction, providing significant advantages over single-mode cavities. We then generalise this approach to show that engineered coupling between states of the emitter can equivalently 'hide' the emitter from the photon, ultimately allowing the extraction efficiency to approach its fundamental upper limit. The principles proposed in this work can be applied in multiple ways to any emitter-cavity system, paving the way to surpassing the traditional limitations with technologies that exist today.