Theory of single-photon emission from neutral and charged excitons in a polarization-selective cavity

Single-photon sources based on neutral or charged excitons in a semiconductor quantum dot are attractive resources for photonic quantum computers and simulators. To obtain indistinguishable photons, the source is pumped on resonance with polarized laser pulses, and the output is collected in orthogonal polarization. However, for sources featuring vertical emission of light, 50% of the emitted photons are unavoidably lost in this way. Here, we theoretically study the quantum dynamics of an exciton embedded in an asymmetric vertical cavity that favors emission in a specific polarization. We identify the configuration for optimal state initialization and demonstrate a path toward near-unity polarized efficiency. We also derive simple analytical formulas for the photon output in each polarization as a function of the Purcell-enhanced emission rates, which shed light on the physical mechanism behind our results.