Polarized electromagnetic radiation by chiral media with time-dependent chiral chemical potential

We investigate photon production from media characterized by a time-dependent chiral chemical potential μ₅(t). We first consider the chiral anomaly as a small perturbation and show that μ₅→ 2γ process generates non-polarized radiation, as the probabilities of producing right and left-handed photons are equal. In chiral semimetal with a vanishing chiral chemical potential but a finite separation of Weyl nodes, Δ(t), the photon production vanishes at the leading order of perturbation theory. We then employ the method of Bogolyubov transformation to obtain the photon spectrum that sums up all powers of μ₅. Employing the exactly solvable model μ₅(t) ∝ A+B(t/τ), we demonstrate that the spectrum exhibits strong circular polarization, whose direction is determined by the sign of μ₅. The spectrum contains resonances associated with the instability of the electromagnetic field in chiral media. We discuss potential phenomenological applications of these findings.