  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 energy state of the dot and using feedback to
control when 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 should be based on the entire
continuous measurement record, but in practice, it may be difficult to do such
processing 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 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.
