How does a quantum superposition respond to gravity? Matter-wave experiments, starting with the neutron interferometer of Colella, Overhauser and Werner, have shown that massive particles pick up gravitationally induced phase shifts. The corresponding effect for light has never been observed at the quantum level, although Stodolsky (1979) and Tanaka (1983) proposed it decades ago. Photons are fundamentally interesting probes: as relativistic particles, they complement matter-wave experiments; they make interferometers up to satellite scales possible; and entangled multi-photon states give signals with no classical counterpart.
In this talk, I will give an overview of the experimental platforms that aim to observe gravitational phase shifts on light and what a successful measurement might teach us. I will then present recent progress on the GRAVITES interferometer, designed to measure gravitationally induced phase shifts on maximally path-entangled states. Finally, I will outline the path towards future experiments testing quantum field theory in curved spacetime.