Sources of single photons are key elements in the study of basic quantum optical concepts and applications in quantum information science. Among the different sources available, semiconductor quantum dots excel with their straight forward integrability in semiconductor based on-chip solutions and the potential that photon emission can be triggered on demand. Usually, the photon emission event is part of a cascaded biexciton-exciton emission scheme. Important properties of the emitted photon such as polarization and time of emission are either probabilistic in nature or pre-determined by electronic properties of the system. In this work, we study the direct two-photon emission from the biexciton. We show that emission through this higher-order transition provides a much more versatile approach to generate a single photon. In the scheme we propose, the two-photon emission from the biexciton is enabled by a laser field (or laser pulse) driving the system into a virtual state inside the band gap. From this intermediate virtual state, the single photon of interest is then spontaneously emitted. Its properties are determined by the driving laser pulse, enabling all-optical on-the-fly control of polarization state, frequency, and time of emission of the photon.
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