Synthetic and cosmological axion hybridization: Entangled photons, Hanbury Brown–Twiss, and quantum beats

In this article it is argued that synthetic axions, emergent collective excitations in topological insulators or Weyl semimetals, hybridize with the cosmological axion, a compelling dark matter candidate via a common two-photon decay channel since they both couple to electromagnetic fields via a Chern-Simons term. We point out an analogy to a V-type three-level system with the two upper levels identified with the synthetic and cosmological axions decaying into a two-photon state. The Weisskopf-Wigner theory of spontaneous decay in multilevel atoms is complemented and extended to describe the dynamics of hybridization. The final two-photon state features both kinematic and polarization entanglement and displays quantum beats as a consequence of the interference between the decay paths. An initial population of either axion induces a population of the other via hybridization. Consequently, a dark matter axion condensate induces a condensate of the synthetic axion, albeit with small amplitude. We obtain a momentum- and polarization-resolved Hanbury Brown-Twiss (HBT) second-order coherence describing coincident correlated two-photon detection. It exhibits quantum beats with a frequency given by the difference between the energies of the synthetic and cosmological axion and perhaps may be harnessed to detect either type of axion excitations. The case of synthetic axions individually is obtained in the limit of vanishing coupling of the cosmological axion and features similar two-photon correlations. Hence second-order (HBT) two-photon coherence may provide an alternative detection mechanism for emergent condensed matter axionic collective excitations. Similarities and differences with parametrically down converted photons are discussed.