We investigate phase shifts in the strong coupling regime of single-atom cavity quantum electrodynamics (QED). On the light transmitted through the system, we observe a phase shift associated with an antiresonance and show that both its frequency and width depend solely on the atom, despite the strong coupling to the cavity. This shift is optically controllable and reaches 140 degrees - the largest ever reported for a single emitter. Our result offers a new technique for the characterization of complex integrated quantum circuits.
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