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 μ 5 ( t ). We first consider the chiral anomaly as a small perturbation and show that μ 5 → 2 γ 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 μ 5 . Employing the exactly solvable model μ 5 ( t ) ∝ A + B tanh ( t / τ ) , we demonstrate that the spectrum exhibits strong circular polarization, whose direction is determined by the sign of μ 5 . The spectrum contains resonances associated with the instability of the electromagnetic field in chiral media. We discuss potential phenomenological applications of these findings.