Third Quantization of the Electromagnetic Field

Each mode j of the electromagnetic field is mathematically equivalent to a harmonic oscillator containing a single hypothetical particle whose excited states correspond to the presence of photons.  In quantum optics, the so-called quadrature operator is defined by x_j=(a_j+a_j^†)/√2,  where a_j and a_j^† are the usual raising and lowering operators.  This allows the definition of a wave function ψ_j(x_j) for the hypothetical particle in quadrature space.  Here we consider an approach in which the wave function is further quantized to produce a field operator.  Since the electromagnetic field is already second-quantized, this corresponds to an additional or third quantization.  This approach was originally introduced as a useful computational technique in quantum optics, but it also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory.  The generalized theory is based on a single parameter γ that is analogous to a mixing angle, such as the Cabibbo angle or the Weinberg angle. The predictions of the generalized theory can be tested using a proposed photon scattering experiment.  The preliminary results of such an experiment will be described.