Harnessing synthetic axions to probe a cosmological axion

Synthetic axions in topological insulators and Weyl semimetals couple to electromagnetism via a topological Chern-Simons term, and so do cosmological axions which are compelling dark matter candidates. Therefore, synthetic and cosmological axions couple indirectly via intermediate states of two photons. We introduce a non-equilibrium effective field theory description of their hybridization or mixing in a medium. We find that a cosmological axion condensate may induce a synthetic axion condensate, and either condensate will induce a topological Chern-Simons condensate in the intermediate photon states. Furthermore, the axion(s) two-point correlation function features an emergent coherence, and displays quantum beats akin to a three level "V" system from a "which-path" interference between the (quasi) normal modes. We analyzed the correlation functions of the intermediate two-photon state and highlighted distinct features that indicate the existence of Chern-Simons condensate. These results may suggest the possibility of harnessing emergent axion quasiparticles in condensed matter systems to probe the cosmological axion as well as new tools to characterize properties of materials with axionic excitations.