  Periodically driven systems are a common topic in modern physics. In optical
lattices specifically, driving is at the origin of many interesting phenomena.
However, energy is not conserved in driven systems, and under periodic driving,
heating of a system is a real concern. In an effort to better understand this
phenomenon, the heating of single-band systems has been studied, with a focus
on disorder- and interaction-induced effects, such as many-body localisation.
Nevertheless, driven systems occur in a much wider context than this, leaving
room for further research. Here, we fill this gap by studying a non-interacting
model, characterised by discrete, periodically spaced energy levels that are
unbounded from above. We couple these energy levels resonantly through a
periodic drive, and discuss the heating dynamics of this system as a function
of the driving protocol. In this way, we show that a combination of stimulated
emission and absorption causes the presence of resonant stable states. This
will serve to elucidate the conditions under which resonant driving causes
heating in quantum systems.
