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Quantum dots (QDs) are semiconductor nanostructures in which a three dimensional potential trap produces an electronic quantum confinement, thus mimicking the behaviour of single atomic dipole-like transitions. However unlike atoms, QDs can be incorporated into solid state photonic devices such as cavities or waveguides that enhance the light-matter interaction. A near unit efficiency light-matter interaction is essential for deterministic, scalable quantum information (QI) devices. In this limit, a single photon input into the device will undergo a large rotation of the polarization of the light field due to the strong interaction with the QD. In this paper we measure a macroscopic (~ 6o) phase shift of light as a result of the interaction with a negatively charged QD coupled to a low quality-factor (Q~ 290) pillar microcavity. This unexpectedly large rotation angle demonstrates this simple low Q-factor design would enable near deterministic light-matter interactions.