The self-assembly of semiconductor quantum dots has opened up new opportunities in photonics. Quantum dots are usually described as 'artificial atoms', because electron and hole confinement gives rise to discrete energy levels. This picture can be justified from the shell structure observed as a quantum dot is filled either with excitons (bound electron-hole pairs) or with electrons. The discrete energy levels have been most spectacularly exploited in single photon sources that use a single quantum dot as emitter. At low temperatures, the artificial atom picture is strengthened by the long coherence times of excitons in quantum dots, motivating the application of quantum dots in quantum optics and quantum information processing. In this context, excitons in quantum dots have already been manipulated coherently. We show here that quantum dots can also possess electronic states that go far beyond the artificial atom model. These states are a coherent hybridization of localized quantum dot states and extended continuum states: they have no analogue in atomic physics. The states are generated by the emission of a photon from a quantum dot. We show how a new version of the Anderson model that describes interactions between localized and extended states can account for the observed hybridization.