"a phonon is a particle of energy hbar*omega, and if you want to increase/reduce the energy of, say, your simple harmonic oscillator, you would add phonons to it one at a time"
Yes, I agree with this statement.
But (since you asked) there is indeed more substance to the theory than this. All of the mathematics is entirely equivalent to having a system of identical particles with bose statistics filling eigenstates of energy omega. If you add another particle, the energy goes up hbar omega. This is entirely equivalent to photons. The only thing unlike "real" (massive) bosonic particles (like pions etc) is that the chemical potential for photons and phonons is zero. Physically, the phonon is just as "real" as the photon! Phonons are quantization of vibrational waves, whereas photons are quantization of electromagnetic waves. There is no fundamental difference really.
Just like photons, you can "fire" a phonon at an atom and excite it (assuming you can match the right transition energy). Maybe it is easier to think about "firing" phonons if you think about wavepackets instead of pure k-states though.
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