If we drive a quantum harmonic oscillator (e.g. starting from its ground state) at its resonance frequency then it will not just create an excitation in the first excited state but will create a coherent state superposition over all number states. This is why, for instance, we don't use quantum harmonic oscillators as qubits, as we cannot isolate the ground and first excited states from the higher order excitations.
Is there a good classical analogy for why this might be the case? Something similar to how if you try to pluck a guitar string then you won't just excite the fundamental, but will instead also get various contributions from the higher order harmonics? With the guitar string this is a consequence of the way a string is plucked necessarily being a mixture of stationary states, so this isn't an appropriate analogy in this case.