Photon self-interaction through gravitons and axions

In this work, we propose to employ the concept of photon self-interaction for axion detection. In particular, we derive the interaction Hamiltonian for photons via axions in a ring cavity. We show that when the incoming photons are considered in plane-wave basis, the interaction vanishes. However, when the realistic case of photon wavepackets are assumed, a self-interaction whose strength is proportional to the size of the wavepacket and the cavity length exists. Under specific conditions, we find that the axion-mediated interaction dominates the gravitationally induced self-interaction. We discuss the implications of this setup for axion detection, focusing on the range of axion mass, $10^{-10}~\text{eV}<m_a<10^{-4}~\text{eV}$ for which the best accuracy of coupling constants is constrained in some cases to $g_{a\gamma \gamma}> 9 \times 10^{-12}~ \text{GeV}^{-1}$.