Experimental test of the third quantization of the electromagnetic field

Each mode $j$ of the electromagnetic field is mathematically equivalent to a harmonic oscillator with wave function ${\ensuremath{\psi}}_{j}({x}_{j})$ in quadrature representation. An approach was recently introduced which further quantized produce operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\psi}}}_{j}({x}_{j})$ [J. D. Franson, Phys. Rev. A 104, 063702 (2021)]. This allows generalization quantum optics and electrodynamics based on an unknown mixing angle $\ensuremath{\gamma}$ that somewhat analogous Cabibbo or Weinberg angle. The theory conventional for $\ensuremath{\gamma}=0$, while it predicts inelastic photon scattering process $\ensuremath{\gamma}\ensuremath{\ne}0$. Here we report results optical experiment set upper bound $|\ensuremath{\gamma}|\ensuremath{\le}1.93\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ rad at 99% confidence level, provided particles created by have negligible mass. High-energy experiments would be required test if mass these very large.