Can one produce a single photon? Yesterday it was stated in this site that a nucleus oscillating in a crystal lattice (may) produces a single photon. I thought that conservation of (angular) momentum requires the production of at least 2 photons, can someone please explain if that is true and how you produce one single photon, expecially considering the thermal radiation produced by the oscillation of a nucleus?
Edit:
I realize that referring to crystal lattices hugely complicates matters, so I'll ask the general question: suppose we have  an individual free charge and we make it oscillate at frequency k Hz on the z axis. How many photons can be emitted? if one is possible what happens to conservation of momentum? What determines the exact direction of the MF oscillation and propapation ?
 A: Let's take the concrete example of a heteronuclear diatomic molecule. This is probably as close as we can come to an ideal harmonic oscillator. To a good approximation the selection rule for the vibrational transition is:
$$ \Delta v = \pm 1 $$
(the anharmonicity in the internuclear potential means that other transitions do occur, but these have a low probability and can usually be ignored).
But in most cases a pure vibrational transition cannot occur precisely because of the conservation of angular momentum. There is a further selection rule:
$$ \Delta J = \pm 1 $$
That is, the transition is rovibrational so both the vibrational and rotational quantum numbers must change at the same time. This is because the angular momentum of the diatom molecule must change by the opposite of the photon spin to conserve angular momentum.
In combined electronic/rovibrational transitions the rotational quantum number can remain unchanged, i.e. $\Delta J = 0$ leading to the Q-branch in the spectrum, but only if the angular momentum of the excited state differs from the ground state by $\pm \hbar$. In this case the angular momentum of the electron state changes by the opposite of the photon spin.
I've chosen a specific example because your question:

Suppose we have an individual free charge and we make it oscillate at frequency k Hz on the z axis

is too vague to be answered. You need to consider what creates the potential within which the charge is oscillating, and what creates the potential will be involved in the conservation of angular momentum. In the case I describe it is the diatomic molecule that changes state to conserve angular momentum, and in the case of the lattice it is the lattice that conserves angular momentum.
