A few months ago I asked about phonons. I got some very good answers but I still have difficulty getting an intuition for phonons, while somehow photons, which in many ways are similar and which I realize I hardly understand anything about, seem more accessible to intuition.
In Ron Maimon's answer to the question "What exactly is a quantum of light?" he asserts that
A quantum of light of wavelength λ is the minimum amount of energy which can be stored in an electromagnetic wave at that wavelength
the classical wave is a superposition of a large number of photons
Translating this to vibrations in a crystal lattice, could we say that a phonon is the minimal amount of energy which can be stored in an lattice vibration in a given mode and that a classical vibration is a superposition of a large number of phonons?
I hope I am correct when I say that the electromagnetic field can interact with matter through the absorption of a photon, and it is this interaction that makes the photon into something particle-like. Do we have the same for phonon-interactions? I.e. that when a crystal vibration interacts with matter it does so by the creation/destruction of whole phonons at a time, which may also get absorbed at more or less precise locations, e.g. the energy of a single phonon is absorbed by a localized electron.
Finally I would like to understand how phonon exchange can effectively establish an attractive force between electrons, but I cannot say I have any intuition for how photons mediate the electromagnetic force either. I am afraid that for the moment this is beyond the scope of my background.