Experimental test of the third quantization of the electromagnetic field

Abstract: Each mode $\small{j}$ of the electromagnetic field is mathematically equivalent to a harmonic oscillator described by a wave function $\small{\psi_j(x_j)}$ in the quadrature representation. An approach was recently introduced in which the wave function $\small{\psi_j(x_j)}$ was further quantized to produce a field operator $\small{{\hat \psi}_j(x_j)}$ [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 $\small{\gamma}$ that is somewhat analogous to the Cabibbo angle or the Weinberg angle. The theory is equivalent to conventional quantum electrodynamics if $\small{\gamma=0}$, while it predicts a new form of inelastic photon scattering if $\small{\gamma\neq0}$. Here we report the results of an optical scattering experiment that set an upper bound of $\small{\gamma\leq 1.93 \times 10^{-4}}$ at the 99% confidence level, provided that the particles created by the field operator $\small{{\hat \psi}_j(x_j)}$ have negligible mass. High-energy experiments would be required to test the theory if the mass of these particles is very large.