Frame dragging and the Hong-Ou-Mandel dip: Gravitational effects in multiphoton interference

Applying quantum field theory on a classical, curved space-time has led to the enthralling theoretical predictions of, e.g., black hole evaporation and particle creation in the early, expanding universe. However, the prospects of observing such in the near to mid future seem far from practical. This is discouraging because extrapolation of general relativity "down to the Hilbert space level," though expected, carries no empirical support as of yet. On the other hand, fueled by the continuing developments in quantum technology, there has been growing interest in the prospect of observing more modest effects of general relativity at the level of quantum interference phenomena. Motivated by these recent developments, in this work, we investigate the Hong-Ou-Mandel (HOM) effect-a two-photon quantum-interference effect-in the space-time of a rotating spherical mass. In particular, we propose and analyze a common-path setup restricted to the surface of the Earth and show that, in principle, gravitational frame dragging induces observable shifts in the two-photon HOM dip. For completeness and correspondence with current literature, we also analyze the emergence of gravitational time dilation, for a dual-arm interferometer. The formalism thus presented establishes a basis for encoding general-relativistic effects into local, multiphoton, quantum-interference experiments. We also consider signatures of noninertial reference-frame effects on two-photon interference such as, e.g., the Sagnac effect induced by Earth's rotation, which seems detectable with current quantum-optical technology. This can be viewed as a stepping-stone towards the more ambitious goal of observing gravitational frame dragging at the level of individual photons.