Enhancement of dark photon haloscope sensitivity with degenerate modes: Toward axion-level form factor and polarization determination

The dark photon has been postulated as a potential constituent of dark matter, exhibiting notable similarities to the axion. The primary distinction between the two particles lies in the nature of their respective fields: the dark photon field is a vector field with a polarization direction that remains undetermined. This work explores the prospect of utilizing three degenerate modes for scanning the three dimensions of space in order to mitigate the low form factor expected in the detection of the dark photon due to their unknown polarization. The employment of a haloscope with three orthogonal and degenerate modes in conjunction with the coherent sum of signals is demonstrated in this work in order to enhance the dark photon form factor up to the axion form factor, and to determine the direction of the dark photon polarization vector. We show in this manuscript that the maximum form factor is achieved in cavities of cubic, spherical, and cylindrical geometries, considering the introduction of tuning elements. To achieve this adequately, some conditions reviewed in this article must be fulfilled in the resonant cavity, leading to uncertainties in the final measurement. Finally, this technique can allow the simultaneous search for dark matter axions and dark photons, and to the knowledge of the authors, the method shown in this work is the most effective one for detecting dark photons with microwave resonant cavities.