Probing dynamical axion quasiparticles with two-photon correlations

Dynamical axion (quasi) particles are emergent collective excitations in topological magnetic insulators that break parity and time reversal invariance or in Weyl semimetals. They couple to electromagnetism via a topological Chern-Simons term, leading to their decay into two photons. We extend the Weisskopf-Wigner formulation of atomic spontaneous emission to the quantum field theory of dynamical axion quasiparticles, allowing us to obtain the quantum two-photon state emerging from axion decay in real time. This state features \emph{hyperentanglement} in momentum and polarization with a distinct polarization pattern, a consequence of the parity and time reversal breaking of the axion-photon interaction. Polarization aspects of this two-photon state are studied by introducing quantum Stokes operators. Whereas the two-photon quantum state features vanishing \emph{averages} of the degree of polarization and polarization asymmetry, there are non-trivial momentum correlations of the Stokes operators. In particular momentum correlations of the \emph{polarization asymmetry} can be obtained directly from coincident momentum and polarization resolved two photon detection. Correlations of Stokes operators are directly related to momentum and polarization resolved Hanbury-Brown Twiss second order coherences. This relationship suggests two-photon correlations as a direct probe of dynamical axion quasiparticles. Similarities and differences with parametrically down converted photons and other systems where spontaneous emission yield hyperentangled two photon states are recognized, suggesting experimental avenues similar to tests of Bell inequalities to probe dynamical axion quasiparticles with coincident two photon detection.