Signatures of Quantum Gravity in the Gravitational Self-Interaction of Photons

We propose relativistic tests of quantum gravity using the gravitational self-interaction of photons in a cavity. We demonstrate that this interaction results in a number of quantum gravitational signatures in the quantum state of the light that cannot be reproduced by any classical theory of gravity. We rigorously assess these effects using quantum parameter estimation theory and discuss simple measurement schemes that optimally extract their signatures. Crucially, the proposed tests are free of QED photon-photon scattering, are sensitive to the spin of the mediating gravitons, and can probe the locality of the gravitational interaction. These protocols provide a new avenue for studying the quantum nature of gravity in a relativistic setting.

Figure 1

(a) Superpositions of different photon numbers result in superpositions of spacetime geometries if gravity is quantum, resulting in quantum gravitational signatures in the state of the light. (b) Cavity geometry considered, where the dominant gravitational interaction is between the two long arms, $L\gg w$. (c),(d) Near-optimal measurement schemes for observing signatures of quantum gravity in (c) the interference between a pair of cavities or (d) non-Gaussianity in the phase quadratures of photons exiting a single cavity. ${\widehat{U}}_{\mathrm{QG}}$ represents the system in (b).