• spacetime fuzziness
• Quantum Gravity
• phenomenology
• interferometry
• correlations

This master thesis project is a phenomenological work on a putative Quantum Gravity effect, the spacetime fuzziness. After a general discussion about Quantum Gravity phenomenology and a review of the theoretical evidences leading to such an effect, a theoretical model describing spacetime fuzziness and an experimental proposal devoted to its detection are discussed. The phenomenological model is based on stochastic fluctuations of the tetrad field. The propagation of a minimally coupled electromagnetic field is studied in such a stochastic spacetime, and a differential equation for the two point correlation of the electromagnetic field is obtained in a perturbative way. This equation is then reinterpreted in a way which makes is applicable also to complex interferometric apparatuses, such as the one proposed here. This is based on a particular kind of cavity, called sloshing cavity, which allows for a continuous and dynamical switching between two configurations, characterized by different spacetime correlation. This switching is possible if in the cavity an amplitude modulated light is injected. The whole apparatus is then composed by an interferometric setup where the two arms are two identical sloshing cavities. This setup is analysed in detail and input-output relations are provided both for the unperturbed and for the perturbed electromagnetic field, the last one being generated by spacetime vibrations. Lastly, the possible noises affecting this apparatus are briefly discussed and some proposals to reduce their contribution to a quantum spacetime noise measurement are qualitatively described.