tech99 said:
I was thinking that a semiconductor laser is close to electron/photon interaction.
One must distinguish between "interaction" and "interference" (or equivalently "superposition").
An interaction is a term in the Lagrangian of the quantum field theory (and as we discuss photons there's no other way than to use relativistic quantum field theory and the Standard Model!), and of course, in QED there's an interaction term between the electron and photon fields since of course the electromagnetic interaction is described as a U(1)-gauge theory with the electric charge as the gauge coupling. The corresponding interaction term is ##\propto e \hat{A}^{\mu} \bar{\hat{\psi}} \gamma_{\mu} \hat{\psi}##, where ##\psi## is the Dirac-spinor field of electrons (or any other charged particles you like to describe concerning electromagnetism).
Interference occurs due to the superposition principle for Hilbert-space vectors, i.e., if you have two Hilbert-space vectors ##|\psi_1 \rangle## and ##|\psi_2 \rangle## you can usually also define another vector ##\lambda_1 |\psi_1 \rangle+ \lambda_2 |\psi_2 \rangle##.
However, this is pure math, and there's also physics in Quantum Theory, which may restrict the possibility to make sense of some kinds of superpositions, i.e., for physical reasons it can be that some superpositions of state kets are "evil", making the theory nonsensical. If for physical reasons some superpositions are "forbidden", one calls it a "superselection rule", i.e., some physics selects these particular superpositions as "forbidden".
One very fundamental superselection rule is the charge superselection rule. Since electromagnetism is a local gauge theory, only gauge invariant mathematical objects are observable quantities, and since the gauge transformations for the matter fields (e.g., for electrons in QED ##\hat{\psi}(x) \rightarrow \exp(+\mathrm{i} e \chi(\vec{x})) \hat{\psi}(x)##, \quad ##\hat{A}^{\mu} \rightarrow \hat{A}^{\mu}+\partial^{\mu} \chi##) involve the gauge coupling. Note that it occurs in the transformation of the matter fields but not in that of the gauge fields, but that's only because in QED we deal with an Abelian U(1) gauge symmetry, which implies that from QED alone there's no reason for any kind of charge quantization, i.e., in principle the gauge coupling can be different to any particle species, and there's no reason that all particles have charges in integer multiples of the elementary charge ##e## (or ##e/3## for tha quarks).
However, to build gauge-invariant states from superpositions of other states the involved particles should all have the same charge, such that the states have a well-defined gauge-transformation property. Now an electron carries charge ##-1## (in units of the elementary charge ##e##), while a photon carries charge ##0##, and thus you must not use superpositions of single-electron and single-photon states.
Another superselection rule is the spin superselection rule, according to which one cannot superimpose states of integer spin with states of half-integer spin, because otherwise a rotation around ##2 \pi## don't make sense anymore. Another reason, related to this, is that there shouldn't be superpositions between bosonic and fermionic states.
