  We consider ultracold atoms trapped in a toroidal trap with an azimuthal
lattice for utility as a macroscopic simulator of quantum optics phenomena. We
examine the dynamics induced by the adiabatic introduction of the lattice that
serves to couple the normal modes, as an analog of a laser field coupling
electronic states. The system is found to display two distinct behaviors,
manifest in the angular momentum - coherent oscillation and self-trapping -
reminiscent of non-linear dynamics, yet not requiring interatomic interactions.
The choice is set by the interplay of discrete parameters, the specific initial
mode and the periodicity of the lattice. However, rotation can cause continuous
transition between the two regimes, causing periodic quenches and revivals in
the oscillations as a function of the angular velocity. Curiously, the impact
of rotation is determined entirely by the energy spectrum in the absence of the
lattice, a feature that can be attributed to adiabaticity. We assess the
effects of varying the lattice parameters, and consider applications in
rotation sensing.
