Long-range atomic interactions for novel quantum technologies

Atomic interactions have a wide range of potential applications in quantum technology but are, unfortunately, usually relatively short-range. In this thesis a novel approach to quantising the electromagnetic field in the presence of two-sided semi-transparent mirrors with finite transmission, reflection and absorption rates is presented. The image-detector method allows one to correctly reproduce the appropriate dynamics of wave packets in the presence of semi-transparent mirrors by mapping onto analogous free-space scenarios meaning photons are characterised as they are in free space. Moreover, radiating atoms in the presence of semi-transparent mirrors exhibit modified spontaneous emission rates due to boundary conditions imposed on the electromagnetic field. Through the image-detector method mirror-mediated dipole-dipole interactions are predicted which modify atomic spontaneous emission rates. The spontaneous emission rates explicitly depend on the optical properties of the semi-transparent mirror and these mirror-mediated dipole-dipole interactions are considered to be long range, as atoms placed several wavelengths from the mirror still exhibit modified spontaneous emission rates. In addition, the model readily extends to describe optical cavities. The results presented in this thesis are expected to pave the way for the modelling of more complex scenarios and for designing novel photonic devices for quantum technology applications, such as non-invasive glucose-sensing technology.