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 ψⱼ(xⱼ) in the quadrature representation. An approach was recently introduced in which ψⱼ(xⱼ) was further quantized to produce a field operator ˆψⱼ(xⱼ) [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 γ that is somewhat analogous to the Cabibbo angle or the Weinberg angle. The theory is equivalent to conventional quantum electrodynamics for γ=0, while it predicts a new form of inelastic photon scattering for γ≠0. Here we report the results of an optical scattering experiment that set an upper bound of |γ|≤1.93×10⁻⁴ rad at the 99% confidence level, provided that the particles created by the operator ˆψⱼ(xⱼ) have negligible mass. High-energy experiments would be required to test the theory if the mass of these particles is very large.