Gravitational redshift of broadband relativistic quantum photons

Abstract

We employ linearized quantum gravity to study gravitational redshift of photons in the context of relativistic and quantum physics, where photons interact in flat spacetime with a classical massive body via graviton exchange. We find that gravitational redshift, as predicted by general relativity, occurs only in the case of localized photons with a well defined momentum that interact with a classical source of gravitons. On the contrary, photons initially prepared in states with nonclassical features, such as quantum coherence in the position degree of freedom, witness no well-defined redshift in general. Our work not only shows that gravitational redshift can be found in flat spacetime as a consequence of the interaction of quantum fields, but it also challenges the robustness of one of the most important predictions of general relativity, furthermore indicating that deviations from the theory can already be observed at low energies using highly nonclassical photonic states.

Figures (3)

• Figure 1: Schematic figure of the setup. Photons propagating in weakly curved spacetime are viewed as field excitations that interact with a source (e.g., planet) via graviton exchange.
• Figure 2: Redshift of nonclassical states: Frequency comb with envelope. If the ratio of the comb spacing $d_0$ and the photon size $\sigma$ is sufficiently small, the photon can witness redshift.
• Figure 3: Pictorial depiction of the scenario of interest: two users Alice (A) and Bob (B) exchange a photon in flat spacetime with weak gravitational perturbations (here represented as two observers being located far away from a planet). The photon interacts with the gravitons (here represented by the ondulated perturbations along the path of the photon).