Photon self-interaction through gravitons and axions

Abstract 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, $$10^{-10}~\text {eV}&lt;m_a&lt;10^{-4}~\text {eV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:mtext>eV</mml:mtext> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:mtext>eV</mml:mtext> </mml:mrow> </mml:math> for which the best accuracy of coupling constants is constrained in some cases to $$g_{a\gamma \gamma }&gt; 9 \times 10^{-12}~ \text {GeV}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mi>a</mml:mi> <mml:mi>γ</mml:mi> <mml:mi>γ</mml:mi> </mml:mrow> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mn>9</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:msup> <mml:mtext>GeV</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> .