We know that a time dependent Hamiltonian can create particles. We know this for instance from field theory in curved spacetime, where for instance in an expanding or contracting universe creation and annihilation of particles can take place.
My question is, is it possible for a particle to be created in a scenario where the Hamiltonian is a periodic function of time (i.e are there particles at the end of the period)? So this would be asking, if the universe expanded and then contracted back to its original size, following say a sine curve, could particles content have changed at the end of it? In more quantum mechanical terms, suppose I have a Hamiltonian $H_0 f(t)$ where $f(t)$ is periodic in time and the initial state is the ground state of $H_0$. Would I have an excited state at the end of one period? I know for instance for Rabbi oscillation I would be back at the same state. But is it always true and if so, is there a general proof or argument for a periodic (or time-symmetric) Hamiltonian?