Induced Circular Polarization on Photons Due to Interaction with Axion-Like Particles in Rotating Magnetic Field of Neutron Stars

We investigate how the photon polarization is affected by the interaction with axion-like particles (ALPs) in the rotating magnetic field of a neutron star (NS). Using quantum Boltzmann equations the study demonstrates that the periodic magnetic field of millisecond NSs enhances the interaction of photons with ALPs and creates a circular polarization on them. A binary system including an NS and a companion star could serve as a probe. When the NS is in front of the companion star with respect to the earth observer, there is a circular polarization on the previously linearly polarized photons as a result of the interaction with ALPs there. After a half-binary period, the companion star passes in front of the NS, and the circular polarization of photons disappears and changes to linear. The excluded parameter space for a millisecond NS with 300~Hz rotating frequency, highlights the coupling constant of $1.7\times {10}^{-11}{\text{GeV}}^{-1}\le g_{a\gamma \gamma }\le 1.6\times {10}^{-3}{\text{GeV}}^{-1}$ for the ALP masses in the range of $7\times {10}^{-12}\text{ eV}\le m_a\le 1.5\times {10}^3\text{ eV}$.