Experimental test of the third quantization of the electromagnetic field

TL;DR

This paper tests a novel third quantization approach to the electromagnetic field by conducting an optical scattering experiment, setting an upper bound on the mixing angle parameter that distinguishes it from conventional quantum electrodynamics.

Contribution

The study provides the first experimental bounds on the third quantization of the electromagnetic field, extending quantum electrodynamics with a new mixing angle parameter.

Findings

Set an upper bound of γ ≤ 1.93 × 10^{-4} at 99% confidence level.

No deviation from conventional QED observed within experimental sensitivity.

Suggests high-energy experiments are needed to explore large particle masses.

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.