Rotation-sensitive quench and revival of coherent oscillations in a ring lattice

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 nonlinear 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.