Experimental test of the third quantization of the electromagnetic field

Abstract

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