Probing dynamical axion quasiparticles with two-photon correlations

TL;DR

The paper develops a quantum-field-theoretic extension of the Weisskopf-Wigner framework to model dynamical axion quasiparticles decaying into two photons through a topological Chern-Simons coupling. It derives the real-time two-photon state, revealing momentum-polarization hyperentanglement and a polarization pattern tied to parity and time-reversal breaking, with a Lorentzian spectral envelope governed by the axion decay width $\Gamma$ and a Lamb shift $\Delta$. Quantum Stokes operators are introduced to quantify polarization properties, revealing vanishing average polarization but nonzero momentum correlations that map onto momentum- and polarization-resolved Hanbury-Brown Twiss coherences. The results offer direct observational signatures for dynamical axions via coincident two-photon detection and draw connections to spontaneous parametric down-conversion, suggesting experimental routes including Bell-inequality tests in topological materials. The work provides a framework for probing axion electrodynamics in condensed-matter systems and outlines future directions for accessing spatio-temporal correlation signatures and alternative decay channels.

Abstract

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.

Figures (4)

• Figure 1: Transitions $|\phi\rangle \Leftrightarrow |\{\kappa_i\}\rangle \neq |\phi\rangle$, induced by the interaction Hamiltonian $H_I$. The set of states $|\{\kappa_i\}\rangle$ belong to a continuum.
• Figure 2: Transitions $|1^{\phi}_{\vec{k}}\rangle \Leftrightarrow |\gamma\gamma\rangle \equiv |1_{\vec{k}_1,\lambda_1};1_{\vec{k}_2,\lambda_2}\rangle$, with $\vec{k}_2=\vec{k}-\vec{k}_1$ induced by the interaction Hamiltonian $H_I$ (\ref{['HIcs']}).
• Figure 3: Second order self-energy diagram.
• Figure 4: Non (RWA) contributions: fig. (a) is a vacuum diagram, fig. (b) is a disconnected diagram with the single axion quasiparticle and vacuum correction. Wiggly lines are photon lines, solid lines correspond to a single axion particle. These diagrams yield a phase $e^{i\Delta E_0 t}$, with $\Delta E_0$ the renormalization of the vacuum energy.