Continuous measurements with feedback can improve single-photon probability

We propose a technique to improve the probability of single-photon emission with an electrically pumped quantum dot in an optical microcavity, by continuously monitoring the dot’s energy state and using feedback to control whether to stop pumping. The goal is to boost the probability of single-photon emission while bounding the probability of two or more photons. We model the system by a stochastic master equation that includes post-measurement operations. Ideally, feedback will be based on the entire continuous measurement record, but in practice, it may be difficult to process such a protocol in real time. We show that even a simple threshold-based feedback scheme using measurements at a single time can improve performance over deterministic (open-loop) pumping. This technique is particularly useful for strong dot-cavity coupling strength with lower rates of pumping, as can be the case for electrical pumping. It is also numerically tractable since we can perform ensemble averaging with a single master equation rather than averaging over a large number of quantum trajectories.