Achieving strong coupling between a single ion and a cavity is an important condition for cavity quantum electrodynamics, mainly for its applications in quantum networks, quantum computing and quantum interfaces. While strong coupling has been achieved in various physical systems, so far it remained elusive for single atomic ions. In this thesis I present the first observation of strong coupling between a single ion and an optical cavity. Our system is a hybrid system where a fibre based Fabry-Pérot cavity was incorporated to a 3D Paul trap. The position of the ion, relative to the cavity mode, was adjusted by applying additional rf signals on the radial electrodes of the trap, in order to maximise the coupling between the ion and the cavity. The coupling strength was measured to be g = 2π × (12.3±0.1) MHz, which exceeds both the atomic decay rate, γ = 2π × 11.5 MHz, and the cavity decay rate, κ = 2π × (4.1 ± 0.1) MHz, placing the ion-cavity coupling in the strong coupling regime. Cavity assisted Raman spectroscopy was used to precisely characterize the ion-cavity coupling strength, and observe a spectrum featuring the normal mode splitting in the cavity transmission due to the ion-cavity interaction. Due to geometric constraints in our trap, Doppler cooling was not optimal along the cavity axis, hindering the localisation of the ion and thus its coupling to the cavity. To improve the localisation of the ion, cavity cooling was used to efficiently cool the ion along the cavity axis. By using cavity cooling, we obtain an enhanced ion-cavity coupling of g0 = 2π × (16.7±0.1) MHz, compared with g0 = 2π × (15.2±0.1) MHz when using only Doppler cooling
