Vector potential quantization and the photon intrinsic electromagnetic properties towards nondestructive photon detection
Résumé
We employ here the enhancement of the vector potential amplitude quantization at a single
photon state. The analysis of the general solution of the vector potential, obtained by resolving
Maxwell's equations, implies that the amplitude is proportional to the angular frequency. The
photon vector potential function αkλ<(r,t) can be written in the plane wave representation
satisfying the classical wave propagation equation, Schrödinger's equation for the energy with
the relativistic massless field Hamiltonian and a linear time-dependent equation for the vector
potential amplitude operator. Thus, the vector potential αkλ<(r,t) with the quantized amplitude
may play the role of a real wave function for the photon in a nonlocal representation that can be
suitably normalized. We then deduce that the amplitudes of the electric and magnetic fields,
respectively, of a single free photon are proportional to the square of the angular frequency. This
might open perspectives for the development of nondestructive photon detection methods based
on the influence of the electric and/or magnetic fields of photons on the energy levels of atoms
and molecules.