Asymmetric two-photon response of an incoherently driven quantum emitter

Quantum emitters promise to emit exactly one photon with high probability when pumped by a laser pulse. However, even in ideal systems, re-excitation during a laser pulse causes the consecutive emission of two photons, thus limiting the single-photon purity. Although the probability and properties of re-excitation are largely determined by the optical excitation method, until now only resonant driving has been studied. Here, we demonstrate qualitative differences in the process arising from phonon-assisted excitation -- a scheme standing out for its robustness and straightforward spectral suppression of scattered laser light while preserving highly indistinguishable emission. In contrast to previous studies under resonant driving, we measure not only the $g^{(2)}(0)$ as a function of pulse length but also resolve the distinct temporal and spectral shape of each of the photons, report an asymmetric two-photon spectrum and uncover correlations between the emission time and wavelength, which are unique to phonon-assisted pumping. On the fundamental side, we show how the spectrum stemming from re-excitation provides direct access to the Rabi frequency of an incoherently driven quantum dot. On the application side, we use the asymmetric spectral response to selectively suppress multiphoton noise from re-excitation, ensuring a high-single photon purity regardless of the laser pulse length and thus enhancing implementations across quantum cryptography and quantum computing.