# Pushing Purcell-enhancement beyond its limits

## TL;DR

This paper introduces a novel scheme leveraging cavity birefringence to surpass traditional Purcell enhancement limits, enabling more efficient photon emission from emitter-cavity systems with longer cavities and advanced configurations.

## Contribution

It presents a theoretical and experimental approach to decouple emitter and photon in birefringent cavities, surpassing previous limitations and enabling improved photon extraction efficiency.

## Key findings

- Birefringence mitigates the tradeoff between coupling strength and photon extraction.
- Longer cavities can be used without performance loss due to birefringence.
- Enhanced emission schemes include detuning ground states and chaining multiple states.

## Abstract

Purcell-enhanced emission from a coupled emitter-cavity system is a fundamental manifestation of cavity quantum electrodynamics. Starting from a theoretical description we derive a scheme for photon emission from an emitter coupled to a birefringent cavity that exceeds hitherto anticipated limitations. Based on a recent study and experimental investigation of the intra-cavity coupling of orthogonal polarisation modes in birefringent cavities, we now decouple the emitter and the photon prior to emission from the cavity mode. Effectively, this is "hiding" the emitter from the photon in the cavity to suppress re-excitation, increasing the overall emission through the cavity mirrors. In doing so we show that tailored cavity birefringence can offer significant advantages and that these are practically achievable within the bounds of present-day technology. It is found that birefringence can mitigate the tradeoff between stronger emitter-cavity coupling and efficient photon extraction. This allows for longer cavities to be constructed without a loss of performance -- a significant result for applications where dielectric mirrors interfere with any trapping fields confining the emitter. We then generalise our model to consider a variety of equivalent schemes. For instance, detuning a pair of ground states in a three-level emitter coupled to a cavity in a Lambda-system is shown to provide the same enhancement, and it can be combined with a birefringent cavity to further increase performance. Additionally, it is found that when directly connecting multiple ground states of the emitter to form a chain of coupled states, the extraction efficiency approaches 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 limits of such systems with technologies that exist today.