Optimising finite-time photon extraction from emitter-cavity systems

We develop methods to find the limits to finite-time single photon extraction from emitter-cavity systems. We first establish analytic upper and lower bounds on the maximum extraction probability from a canonical $\Lambda$-system before developing a numeric method to optimise generic output probabilities from $\Lambda$-systems generalised to multiple ground states. We use these methods to study the limits to finite-time photon extraction and the wavepackets that satisfy them, finding that using an optimised wavepacket ranging between a sinusoidal and exponentially decaying profile can considerably reduce photon duration for a given extraction efficiency. We further optimise the rates of quantum protocols requiring emitter-photon correlation to obtain driving-independent conclusions about the effect of system parameters on success probability. We believe that these results and methods will provide valuable tools and insights for the development of cavity-based single photon sources combining high efficiency and high rate.